Relevant bibliographies by topics / Bounded linear operator

Academic literature on the topic 'Bounded linear operator'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Bounded linear operator"

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Kudryashov, Yu L. "Dilatations of Linear Operators." Contemporary Mathematics. Fundamental Directions 66, no. 2 (December 15, 2020): 209–20. http://dx.doi.org/10.22363/2413-3639-2020-66-2-209-220.

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The article is devoted to building various dilatations of linear operators. The explicit construction of a unitary dilation of a compression operator is considered. Then the J -unitary dilatation of a bounded operator is constructed by means of the operator knot concept of a bounded linear operator. Using the Pavlov method, we construct the self-adjoint dilatation of a bounded dissipative operator. We consider spectral and translational representations of the self-adjoint dilatation of a densely defined dissipative operator with nonempty set of regular points. Using the concept of an operator knot for a bounded operator and the Cayley transform, we introduce an operator knot for a linear operator. By means of this concept, we construct the J -self-adjoint dilatation of a densely defined operator with a regular point. We obtain conditions of isomorphism of extraneous dilations and their minimality.
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Nakasho, Kazuhisa, Yuichi Futa, and Yasunari Shidama. "Continuity of Bounded Linear Operators on Normed Linear Spaces." Formalized Mathematics 26, no. 3 (October 1, 2018): 231–37. http://dx.doi.org/10.2478/forma-2018-0021.

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Summary In this article, using the Mizar system [1], [2], we discuss the continuity of bounded linear operators on normed linear spaces. In the first section, it is discussed that bounded linear operators on normed linear spaces are uniformly continuous and Lipschitz continuous. Especially, a bounded linear operator on the dense subset of a complete normed linear space has a unique natural extension over the whole space. In the next section, several basic currying properties are formalized. In the last section, we formalized that continuity of bilinear operator is equivalent to both Lipschitz continuity and local continuity. We referred to [4], [13], and [3] in this formalization.
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Al-Muttalibi, Rana, and Radhi M.A Ali. "Certain types of linear operators on probabilistic Hilbert space." Global Journal of Mathematical Analysis 3, no. 2 (May 24, 2015): 81. http://dx.doi.org/10.14419/gjma.v3i2.4664.

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<p>The purpose of this paper is to introduce some definitions, properties and basic results that show the relation between F-bounded of linear operator in probabilistic Hilbert space and bounded operator in norm. In the paper, we prove that the adjoint operator in probabilistic Hilbert space is bounded. The notion of the continuous operators in probabilistic Hilbert space and some basic results are given. In addition, we note that every operator in probabilistic real Hilbert space is a self-adjoint Operator.</p>
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Mehd, Sadiq A., Salim Dawood Mohsen, and Mohammed J. Fari. "Properties (RB) and (gRB) for Bounded Linear Operators." Journal of Physics: Conference Series 2322, no. 1 (August 1, 2022): 012053. http://dx.doi.org/10.1088/1742-6596/2322/1/012053.

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Abstract In this article, we consider pseudo invertible operators for study of the relationship between the space of relatively regular operators and some generalizations of Weyl and Browder theorems. By using the analysis and representation of pseudo invertible operators, some new properties in connection with Browder’s type theorems, were presented for bounded linear operators T ∈ B(X). These properties, which we refer to as property (RB), imply that All poles of the resolvent of T of finite rank in the typical spectrum are precisely those places of the spectrum for which a reasonably regular operator with its pseudo inverse operator is surjective. (γI – T)† ∈ SU(X), In the usual spectrum, the set of all poles of the resolvent is exactly those points of the spectrum for which we call property (gRB). γI – T is a B-relatively regular operator with its pseudo inverse operator is surjective (γI – T)† ∈ SU(X). In addition, several sufficient and necessary conditions for which properties (RB) and (gRB) hold are given.
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Bajryacharya, Prakash Muni, and Keshab Raj Phulara. "Extension of Bounded Linear Operators." Journal of Advanced College of Engineering and Management 2 (November 29, 2016): 11. http://dx.doi.org/10.3126/jacem.v2i0.16094.

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<p>In this article the problem entitled when does every member of a class of operators T : E → Y admit an extension operator T : X → Y in different approaches like injective spaces, separable injective spaces, the class of compact operators and extension Into C(K ) spaces has-been studied.</p><p><strong>Journal of Advanced College of Engineering and Management,</strong> Vol. 2, 2016, page: 11-13</p>
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Mohsen, Salim Dawood, and Hanan Khalid Mousa. "Another Results Related of Fuzzy Soft Quasi Normal Operator in Fuzzy Soft Hilbert Space." Journal of Physics: Conference Series 2322, no. 1 (August 1, 2022): 012050. http://dx.doi.org/10.1088/1742-6596/2322/1/012050.

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Abstract The goal of this paper, is to introduce another classes of the fuzzy soft bounded linear operator in the fuzzy soft Hilbert space which is a fuzzy soft quasi normal operator, as well as, give some properties about this concept with investigating the relationship among this types of the fuzzy soft bounded linear operator on fuzzy soft Hilbert space with other kinds of fuzzy soft bounded linear operators.
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Djolović, Ivana, Katarina Petković, and Eberhard Malkowsky. "Matrix mappings and general bounded linear operators on the space bv." Mathematica Slovaca 68, no. 2 (April 25, 2018): 405–14. http://dx.doi.org/10.1515/ms-2017-0111.

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Abstract If X and Y are FK spaces, then every infinite matrix A ∈ (X, Y) defines a bounded linear operator LA ∈ B(X, Y) where LA(x) = Ax for each x ∈ X. But the converse is not always true. Indeed, if L is a general bounded linear operator from X to Y, that is, L ∈ B(X, Y), we are interested in the representation of such an operator using some infinite matrices. In this paper we establish the representations of the general bounded linear operators from the space bv into the spaces ℓ∞, c and c0. We also prove some estimates for their Hausdorff measures of noncompactness. In this way we show the difference between general bounded linear operators between some sequence spaces and the matrix operators associated with matrix transformations.
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ASSADI, AMANOLLAH, MOHAMAD ALI FARZANEH, and HAJI MOHAMMAD MOHAMMADINEJAD. "ON THE DECOMPOSITION OF OPERATORS WITH SEVERAL ALMOST-INVARIANT SUBSPACES." Bulletin of the Australian Mathematical Society 99, no. 2 (January 4, 2019): 274–83. http://dx.doi.org/10.1017/s0004972718001363.

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We seek a sufficient condition which preserves almost-invariant subspaces under the weak limit of bounded operators. We study the bounded linear operators which have a collection of almost-invariant subspaces and prove that a bounded linear operator on a Banach space, admitting each closed subspace as an almost-invariant subspace, can be decomposed into the sum of a multiple of the identity and a finite-rank operator.
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Liu, Xiaoji, Miao Zhang, and Yaoming Yu. "Note on the Invariance Properties of Operator Products Involving Generalized Inverses." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/213458.

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We investigate further the invariance properties of the bounded linear operator productAC1 B1 Dand its range with respect to the choice of the generalized inversesXandYof bounded linear operators. Also, we discuss the range inclusion invariance properties of the operator product involving generalized inverses.
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Frank, Michael. "Characterizing C*-algebras of compact operators by generic categorical properties of Hilbert C*-modules." Journal of K-theory 2, no. 3 (March 4, 2008): 453–62. http://dx.doi.org/10.1017/is008001031jkt035.

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AbstractC*-algebras A of compact operators are characterized as those C*-algebras of coefficients of Hilbert C*-modules for which (i) every bounded A-linear operator between two Hilbert A-modules possesses an adjoint operator, (ii) the kernels of all bounded A-linear operators between Hilbert A-modules are orthogonal summands, (iii) the images of all bounded A-linear operators with closed range between Hilbert A-modules are orthogonal summands, and (iv) for every Hilbert A-module every Hilbert A-submodule is a topological summand. Thus, the theory of Hilbert C*-modules over C*-algebras of compact operators has similarities with the theory of Hilbert spaces. In passing, we obtain a general closed graph theorem for bounded module operators on arbitrary Hilbert C*-modules.
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Dissertations / Theses on the topic "Bounded linear operator"

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Turcu, George R. "Hypercyclic Extensions Of Bounded Linear Operators." Bowling Green State University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1386189984.

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Bahreini, Esfahani Manijeh. "Complemented Subspaces of Bounded Linear Operators." Thesis, University of North Texas, 2003. https://digital.library.unt.edu/ark:/67531/metadc4349/.

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For many years mathematicians have been interested in the problem of whether an operator ideal is complemented in the space of all bounded linear operators. In this dissertation the complementation of various classes of operators in the space of all bounded linear operators is considered. This paper begins with a preliminary discussion of linear bounded operators as well as operator ideals. Let L(X, Y ) be a Banach space of all bounded linear operator between Banach spaces X and Y , K(X, Y ) be the space of all compact operators, and W(X, Y ) be the space of all weakly compact operators. We denote space all operator ideals by O.
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O'Connor, B. J. "State diagrams for bounded and unbounded linear operators." Master's thesis, University of Cape Town, 1990. http://hdl.handle.net/11427/18245.

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Bibliography: pages 107-110.
The theme of this thesis is the construction of state diagrams and their implications. The author generalises most of the theorems in Chapter II of Goldberg [Gl] by dropping the assumption that the doin.ain of the operator is dense in X . The author also presents the standard Taylor-Halberg-Goldberg state diagrams [Gl, 61, 66]. Chapters II and III deal with F₊- and F₋-operators, which are generalisations of the ф₊- and ф₋-operators in Banach spaces of Gokhberg-Krein [GK]. Examples are given of F₊- and F₋-operators. Also, in Chapter III, the main theorems needed to construct the state diagrams of Chapter IV are discussed. The state diagrams of Chapter IV are based on states corresponding to F₊- and F₋-operators; in addition state diagrams relating T and T˝ under the assumptions ϒ(T) > 0 and ϒ(T΄) > 0 are derived. Second adjoints are important in Tauberian Theory (see Cross [Cl]). Chapters I and IV are the main chapters. In Chapter I of this thesis the author modifies many of the proofs appearing in Goldberg [Gl), to take account of the new definition of the adjoint.
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Li, Xiaochun. "Uniform bounds for the bilinear Hilbert transforms /." free to MU campus, to others for purchase, 2001. http://wwwlib.umi.com/cr/mo/fullcit?p3025634.

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Abbott, Catherine Ann. "Operators on Continuous Function Spaces and Weak Precompactness." Thesis, University of North Texas, 1988. https://digital.library.unt.edu/ark:/67531/metadc331171/.

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If T:C(H,X)-->Y is a bounded linear operator then there exists a unique weakly regular finitely additive set function m:-->L(X,Y**) so that T(f) = ∫Hfdm. In this paper, bounded linear operators on C(H,X) are studied in terms the measure given by this representation theorem. The first chapter provides a brief history of representation theorems of these classes of operators. In the second chapter the represenation theorem used in the remainder of the paper is presented. If T is a weakly compact operator on C(H,X) with representing measure m, then m(A) is a weakly compact operator for every Borel set A. Furthermore, m is strongly bounded. Analogous statements may be made for many interesting classes of operators. In chapter III, two classes of operators, weakly precompact and QSP, are studied. Examples are provided to show that if T is weakly precompact (QSP) then m(A) need not be weakly precompact (QSP), for every Borel set A. In addition, it will be shown that weakly precompact and GSP operators need not have strongly bounded representing measures. Sufficient conditions are provided which guarantee that a weakly precompact (QSP) operator has weakly precompact (QSP) values. A sufficient condition for a weakly precomact operator to be strongly bounded is given. In chapter IV, weakly precompact subsets of L1(μ,X) are examined. For a Banach space X whose dual has the Radon-Nikodym property, it is shown that the weakly precompact subsets of L1(μ,X) are exactly the uniformly integrable subsets of L1(μ,X). Furthermore, it is shown that this characterization does not hold in Banach spaces X for which X* does not have the weak Radon-Nikodym property.
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Ghassel, Ali. "The radon split of radially acting linear integral operators on h¦2 with uniformly bounded double norms." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/MQ48521.pdf.

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Ugur, Omur. "Boundary Value Problems For Higher Order Linear Impulsive Differential Equations." Phd thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/686691/index.pdf.

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_I The theory of impulsive di®
erential equations has become an important area of research in recent years. Linear equations, meanwhile, are fundamental in most branches of applied mathematics, science, and technology. The theory of higher order linear impulsive equations, however, has not been studied as much as the cor- responding theory of ordinary di®
erential equations. In this work, higher order linear impulsive equations at ¯
xed moments of impulses together with certain boundary conditions are investigated by making use of a Green'
s formula, constructed for piecewise di®
erentiable functions. Existence and uniqueness of solutions of such boundary value problems are also addressed. Properties of Green'
s functions for higher order impulsive boundary value prob- lems are introduced, showing a striking di®
erence when compared to classical bound- ary value problems of ordinary di®
erential equations. Necessarily, instead of an or- dinary Green'
s function there corresponds a sequence of Green'
s functions due to impulses. Finally, as a by-product of boundary value problems, eigenvalue problems for higher order linear impulsive di®
erential equations are studied. The conditions for the existence of eigenvalues of linear impulsive operators are presented. Basic properties of eigensolutions of self-adjoint operators are also investigated. In particular, a necessary and su±
cient condition for the self-adjointness of Sturm-Liouville opera- tors is given. The corresponding integral equations for boundary value and eigenvalue problems are also demonstrated in the present work.
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Hernandez, Michelle Fernanda Pierri. "Funções s-assintoticamente periódicas em espaços de Banach e aplicações à equações diferenciais funcionais." Universidade de São Paulo, 2009. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-19052009-161255/.

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Este trabalho está voltado para o estudo de uma classe de funções contínuas e limitadas f : [0; \'INFINITO\') \'SETA\' X para as quais existe \'omega\' \'> OU =\' 0 tal que \'lim IND. t\' \'SETA\' \'INFINITO\' (f(t + \'omega\') - f(t)) = 0. No decorrer do trabalho, chamaremos estas funções de S-assintoticamente \'omega\'-periódicas. Nós discutiremos propriedades qualitativas para estas funções e algumas relações entre este tipo de funções e a classe de funções assintoticamente \'omega\'-periódicas. Também estudaremos a existência de soluções fracas S-assintoticamente \'omega\'-periódicas para uma classe de primeira ordem de um problema de Cauchy abstrato bem como para algumas classes de equações diferenciais funcionais parciais neutras com retardo não limitado. Algumas aplicações para equações diferenciais parciais serão consideradas
This work is devoted to the study of the class of continuous and bounded functions f : [0 \'INFINIT\') \'ARROW\' X for which there exists \'omega\' > 0 such that \'limt IND.t \'ARROW\' \'INFINIT\'(f(t + \'omega\'!) - f(t)) = 0 (in the sequel called S-asymptotically !-periodic functions). We discuss qualitative properties and establish some relationships between this type of functions and the class of asymptotically \'omega\'-periodic functions. We also study the existence of S-asymptotically \'omega\'-periodic mild solutions for a first-order abstract Cauchy problem in Banach spaces and for some classes of abstract neutral functional differential equations with infinite delay. Furthermore, applications to partial differential equations are given
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Ferroni, Nicola. "Exact Combinatorial Optimization with Graph Convolutional Neural Networks." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/17502/.

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Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose to learn a variable selection policy for branch-and-bound in mixed-integer linear programming, by imitation learning on a diversified variant of the strong branching expert rule. We encode states as bipartite graphs and parameterize the policy as a graph convolutional neural network. Experiments on a series of synthetic problems demonstrate that our approach produces policies that can improve upon expert-designed branching rules on large problems, and generalize to instances significantly larger than seen during training.
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Ware, Griffith Kuskie. "Uniqueness of norm properties of Calkin Algebras." Phd thesis, 2014. http://hdl.handle.net/1885/14510.

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A classical result due to M. Eidelheit and B. Yood states that the standard algebra norm on the algebra of bounded linear operators on a Banach space is minimal, in the sense that the norm must be less than a multiple of any other submultiplicative norm on the same algebra. This de nition does not assume that the arbitrary algebra norm is complete. In cases when the standard algebra norm is, in addition, maximal, it is therefore unique up to equivalence. More recently, M. Meyer showed that the Calkin algebras of a very restricted class of Banach spaces also have unique algebra norms. We generalise the Eidelheit-Yood method of proof, to show that the conventional quotient norm on a larger class of Calkin algebras is minimal. Since maximality of the norm is a presumed property for the class, the norm is also unique. We thus extend the result of Meyer. In particular, we establish that the Calkin algebras of canonical Banach spaces such as James' space and Tsirelson's space have unique algebra norms, without assuming completeness. We also prove uniqueness of norm for quotients of the algebras of operators on classical non-separable spaces, the closed ideals of which were previously studied by M. Daws. One aspect of the Eidelheit-Yood method is a dependence on the uniform boundedness principle. As a component of our generalisation, we prove an analogue of that principle which applies to Calkin algebra elements rather than bounded linear operators. In order to translate the uniform boundedness principle into this new setting, we take the perspective that non-compact operators map certain wellseparated sequences to other well-separated sequences. We analyse the limiting separation of such sequences, using these values to measure the non-compactness of operators and de ne the requisite notion of a bounded set of non-compact operators. In the cases when the underlying Banach space has a Schauder basis, we are able to restrict attention to seminormalised block basic sequences. As a consequence, our main uniqueness of norm result for Calkin algebras relies on the existence of bounded mappings between, and projections onto, the spans of block basic sequences in the relevant Banach spaces.
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Books on the topic "Bounded linear operator"

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Beltiță, Daniel. Lie algebras of bounded operators. Basel: Birkhäuser Verlag, 2001.

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Kubrusly, Carlos S. Spectral Theory of Bounded Linear Operators. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-33149-8.

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Harte, Robin. Invertibility and singularity for bounded linear operators. New York: M. Dekker, 1988.

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Dragomir, Silvestru Sever. Kato's Type Inequalities for Bounded Linear Operators in Hilbert Spaces. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-17459-0.

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Pisier, Gilles. Similarity problems and completely bounded maps. 2nd ed. Berlin: Springer, 2001.

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Similarity problems and completely bounded maps. Berlin: Springer, 1996.

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Christensen, Jens Gerlach. Trends in harmonic analysis and its applications: AMS special session on harmonic analysis and its applications : March 29-30, 2014, University of Maryland, Baltimore County, Baltimore, MD. Providence, Rhode Island: American Mathematical Society, 2015.

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1975-, Sims Robert, and Ueltschi Daniel 1969-, eds. Entropy and the quantum II: Arizona School of Analysis with Applications, March 15-19, 2010, University of Arizona. Providence, R.I: American Mathematical Society, 2011.

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Beltita, Daniel, and Mihai Sabac. Lie Algebras of Bounded Operators (Operator Theory, Advances and Applications, Vol 120). Birkhauser, 2000.

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Beltita, Daniel, and Mihai Sabac. Lie Algebras and Bounded Operators. Birkhauser, 2001.

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Book chapters on the topic "Bounded linear operator"

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Gohberg, Israel, and Seymour Goldberg. "Bounded Linear Operators on Hilbert Spaces." In Basic Operator Theory, 51–103. Boston, MA: Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-5985-5_2.

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Mortad, Mohammed Hichem. "Basic Classes of Bounded Linear Operators." In Counterexamples in Operator Theory, 21–37. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-97814-3_2.

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Kubrusly, Carlos S. "Spectrum of an Operator." In Spectral Theory of Bounded Linear Operators, 27–53. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-33149-8_2.

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Seifert, Christian, Sascha Trostorff, and Marcus Waurick. "Non-Autonomous Evolutionary Equations." In Evolutionary Equations, 259–73. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-89397-2_16.

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AbstractPreviously, we focussed on evolutionary equations of the form $$\displaystyle \left (\overline {\partial _{t,\nu }M(\partial _{t,\nu })+A}\right )U=F. $$ ∂ t , ν M ( ∂ t , ν ) + A ¯ U = F . In this chapter, where we turn back to well-posedness issues, we replace the material law operator M(∂t,ν), which is invariant under translations in time, by an operator of the form $$\displaystyle \mathcal {M}+\partial _{t,\nu }^{-1}\mathcal {N}, $$ ℳ + ∂ t , ν − 1 N , where both $$\mathcal {M}$$ ℳ and $$\mathcal {N}$$ N are bounded linear operators in $$L_{2,\nu }(\mathbb {R};H)$$ L 2 , ν ( ℝ ; H ) . Thus, it is the aim in the following to provide criteria on $$\mathcal {M}$$ ℳ and $$\mathcal {N}$$ N under which the operator $$\displaystyle \partial _{t,\nu }\mathcal {M}+\mathcal {N}+A $$ ∂ t , ν ℳ + N + A is closable with continuous invertible closure in $$L_{2,\nu }(\mathbb {R};H)$$ L 2 , ν ( ℝ ; H ) . In passing, we shall also replace the skew-selfadjointness of A by a suitable real part condition. Under additional conditions on $$\mathcal {M}$$ ℳ and $$\mathcal {N}$$ N , we will also see that the solution operator is causal. Finally, we will put the autonomous version of Picard’s theorem into perspective of the non-autonomous variant developed here.
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Blanchard, Philippe, and Erwin Brüning. "Bounded Linear Operators." In Mathematical Methods in Physics, 275–91. Boston, MA: Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-0049-9_21.

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Blanchard, Philippe, and Erwin Brüning. "Bounded Linear Operators." In Mathematical Methods in Physics, 307–23. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-14045-2_22.

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Zhu, Kehe. "Bounded linear operators." In Mathematical Surveys and Monographs, 1–32. Providence, Rhode Island: American Mathematical Society, 2007. http://dx.doi.org/10.1090/surv/138/01.

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Wong, M. W. "Bounded Linear Operators." In Discrete Fourier Analysis, 107–12. Basel: Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-0348-0116-4_15.

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Eidelman, Yuli, Vitali Milman, and Antonis Tsolomitis. "Bounded linear operators." In Graduate Studies in Mathematics, 55–73. Providence, Rhode Island: American Mathematical Society, 2004. http://dx.doi.org/10.1090/gsm/066/04.

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Kress, Rainer. "Bounded and Compact Operators." In Linear Integral Equations, 15–27. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-0559-3_2.

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Conference papers on the topic "Bounded linear operator"

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"A linear inhomogeneous equation with a Hilfer derivative and a bounded operator." In Уфимская осенняя математическая школа - 2022. 2 часть. Baskir State University, 2022. http://dx.doi.org/10.33184/mnkuomsh2t-2022-09-28.55.

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Akgül, A., and M. Giyas Sakar. "Reproducing kernel functions and bounded linear operator for solving fractional nonlinear boundary value problems." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017). Author(s), 2018. http://dx.doi.org/10.1063/1.5044174.

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Balas, Mark J., and Susan A. Frost. "Adaptive Tracking Control for Linear Infinite Dimensional Systems." In ASME 2016 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/smasis2016-9098.

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Tracking an ensemble of basic signals is often required of control systems in general. Here we are given a linear continuous-time infinite-dimensional plant on a Hilbert space and a space of tracking signals generated by a finite basis, and we show that there exists a stabilizing direct adaptive control law that will stabilize the plant and cause it to asymptotically track any member of this collection of signals. The plant is described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on the Hilbert space of states. There is no state or parameter estimation used in this adaptive approach. Our results are illustrated by adaptive control of general linear diffusion systems.
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Fijalkow, Nathanaël, Bastien Maubert, Aniello Murano, and Moshe Vardi. "Assume-Guarantee Synthesis for Prompt Linear Temporal Logic." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/17.

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Prompt-LTL extends Linear Temporal Logic with a bounded version of the ``eventually'' operator to express temporal requirements such as bounding waiting times. We study assume-guarantee synthesis for prompt-LTL: the goal is to construct a system such that for all environments satisfying a first prompt-LTL formula (the assumption) the system composed with this environment satisfies a second prompt-LTL formula (the guarantee). This problem has been open for a decade. We construct an algorithm for solving it and show that, like classical LTL synthesis, it is 2-EXPTIME-complete.
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Li, Perry Y., and Dongjun Lee. "Passive Feedforward Approach to Bilateral Teleoperated Manipulators." In ASME 2000 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/imece2000-2425.

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Abstract A control scheme for linear dynamically similar bilateral teleoperated manipulator system which ensures that the closed loop system is energetically passive is proposed. Energetic passivity implies that the teleoperated manipulator system is safe to interact with, and that the coupling between the system and any strictly passive environment is stable. The control objective is for the two manipulators in the system to behave in unison under the influence of both the operator and the work environment, while maintaining energetic passivity. The dynamics of the system in unison and its response to the operator and work environment can be specified as kinematic and power scalings. To maintain energetic passivity with feedback and feedforward actions, the proposed control makes use of two fictitious internal energy storages. The result is that when the internal state of the storage elements are suitably initialized, the teleoperated manipulator system achieves asymptotic locking even in the presence of external (bounded) forcing from the operator and work environment.
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Balas, Mark J. "Augmentation of Fixed Gain Controlled Infinite Dimensional Systems With Direct Adaptive Control." In ASME 2020 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/imece2020-23179.

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Abstract Linear infinite dimensional systems are described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on a general Hilbert space of states and are controlled via a finite number of actuators and sensors. Many distributed applications are included in this formulation, such as large flexible aerospace structures, adaptive optics, diffusion reactions, smart electric power grids, and quantum information systems. In this paper, we focus on infinite dimensional linear systems for which a fixed gain linear infinite or finite dimensional controller is already in place. We augment this controller with a direct adaptive controller that will maintain stability of the full closed loop system even when the fixed gain controller fails to do so. We prove that the transmission zeros of the combined system are the original open loop transmission zeros, and the point spectrum of the controller alone. Therefore, the combined plant plus controller is Almost Strictly Dissipative (ASD) if and only if the original open loop system is minimum phase, and the fixed gain controller alone is exponentially stable. This result is true whether the fixed gain controller is finite or infinite dimensional. In particular this guarantees that a controller for an infinite dimensional plant based on a reduced -order approximation can be stabilized by augmentation with direct adaptive control to mitigate risks. These results are illustrated by application to direct adaptive control of general linear diffusion systems on a Hilbert space that are described by self-adjoint operators with compact resolvent.
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Balas, Mark J., and Susan A. Frost. "A Stabilization of Fixed Gain Controlled Infinite Dimensional Systems by Augmentation With Direct Adaptive Control." In ASME 2017 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/smasis2017-3726.

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Linear infinite dimensional systems are described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on a general Hilbert space of states and are controlled via a finite number of actuators and sensors. Many distributed applications are included in this formulation, such as large flexible aerospace structures, adaptive optics, diffusion reactions, smart electric power grids, and quantum information systems. We have developed the following stability result: an infinite dimensional linear system is Almost Strictly Dissipative (ASD) if and only if its high frequency gain CB is symmetric and positive definite and the open loop system is minimum phase, i.e. its transmission zeros are all exponentially stable. In this paper, we focus on infinite dimensional linear systems for which a fixed gain linear infinite or finite dimensional controller is already in place. It is usually true that fixed gain controllers are designed for particular applications but these controllers may not be able to stabilize the plant under all variations in the operating domain. Therefore we propose to augment this fixed gain controller with a relatively simple direct adaptive controller that will maintain stability of the full closed loop system over a much larger domain of operation. This can ensure that a flexible structure controller based on a reduced order model will still maintain closed-loop stability in the presence of unmodeled system dynamics. The augmentation approach is also valuable to reduce risk in loss of control situations. First we show that the transmission zeros of the augmented infinite dimensional system are the open loop plant transmission zeros and the eigenvalues (or poles) of the fixed gain controller. So when the open-loop plant transmission zeros are exponentially stable, the addition of any stable fixed gain controller does not alter the stability of the transmission zeros. Therefore the combined plant plus controller is ASD and the closed loop stability when the direct adaptive controller augments this combined system is retained. Consequently direct adaptive augmentation of controlled linear infinite dimensional systems can produce robust stabilization even when the fixed gain controller is based on approximation of the original system. These results are illustrated by application to a general infinite dimensional model described by nuclear operators with compact resolvent which are representative of distributed parameter models of mechanically flexible structures. with a reduced order model based controller and adaptive augmentation.
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Aiena, Pietro. "Weyl type theorems for bounded linear operators on Banach spaces." In Proceedings of the Fourth International School — In Memory of Professor Antonio Aizpuru Tomás. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814335812_0002.

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9

Glass, John W., and Matthew A. Franchek. "Bounded-Input-Bounded-Output Stability of Nonlinear Feedback Systems in a Volterra Representation." In ASME 2000 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/imece2000-2342.

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Abstract Presented in this paper is a stability condition for a class of nonlinear feedback systems where the plant dynamics can be represented by a finite series of Volterra kernels. The class of Volterra kernels are limited to p-linear stable operators and may contain pure delays. The stability condition requires that the linear kernel is nonzero and that the closed loop characteristic equation associated with the linearized system is stable. Next, a sufficient condition is developed to upper bound the infinity-norm of an external disturbance signal thereby guaranteeing that the internal and output signals of the closed loop nonlinear system are contained in L∞. These results are then demonstrated on a design example. A frequency domain controller design procedure is also developed using these results where the trade-off between performance and stability are considered for this class of nonlinear feedback systems.
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Liu, Chenchen, and Wai Ho Mow. "Bounds on the expected rank of sparse linear operator channel matrices." In 2013 19th Asia-Pacific Conference on Communications (APCC). IEEE, 2013. http://dx.doi.org/10.1109/apcc.2013.6766002.

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Reports on the topic "Bounded linear operator"

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Muelaner, Jody Emlyn. Electric Road Systems for Dynamic Charging. SAE International, March 2022. http://dx.doi.org/10.4271/epr2022007.

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Electric road systems (ERS) enable dynamic charging—the most energy efficient and economical way to decarbonize road vehicles. ERS draw electrical power directly from the grid and enable vehicles with small batteries to operate without the need to stop for charging. The three main technologies (i.e., overhead catenary lines, road-bound conductive tracks, and inductive wireless systems in the road surface) are all technically proven; however, no highway system has been commercialized. Electric Road Systems for Dynamic Charging discusses the technical and economic advantages of dynamic charging and questions the current investment in battery-powered and hydrogen-fueled vehicles.
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Visser, R., H. Kao, R. M. H. Dokht, A. B. Mahani, and S. Venables. A comprehensive earthquake catalogue for northeastern British Columbia: the northern Montney trend from 2017 to 2020 and the Kiskatinaw Seismic Monitoring and Mitigation Area from 2019 to 2020. Natural Resources Canada/CMSS/Information Management, 2021. http://dx.doi.org/10.4095/329078.

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To increase our understanding of induced seismicity, we develop and implement methods to enhance seismic monitoring capabilities in northeastern British Columbia (NE BC). We deploy two different machine learning models to identify earthquake phases using waveform data from regional seismic stations and utilize an earthquake database management system to streamline the construction and maintenance of an up-to-date earthquake catalogue. The completion of this study allows for a comprehensive catalogue in NE BC from 2014 to 2020 by building upon our previous 2014-2016 and 2017-2018 catalogues. The bounds of the area where earthquakes were located were between 55.5°N-60.0°N and 119.8°W-123.5°W. The earthquakes in the catalogue were initially detected by machine learning models, then reviewed by an analyst to confirm correct identification, and finally located using the Non-Linear Location (NonLinLoc) algorithm. Two distinct sub-areas within the bounds consider different periods to supplement what was not covered in previously published reports - the Northern Montney Trend (NMT) is covered from 2017 to 2020 while the Kiskatinaw Seismic Monitoring and Mitigation Area (KSMMA) is covered from 2019 to 2020. The two sub-areas are distinguished by the BC Oil &amp; Gas Commission (BCOGC) due to differences in their geographic location and geology. The catalogue was produced by picking arrival phases on continuous seismic waveforms from 51 stations operated by various organizations in the region. A total of 17,908 events passed our quality control criteria and are included in the final catalogue. Comparably, the routine Canadian National Seismograph Network (CNSN) catalogue reports 207 seismic events - all events in the CNSN catalogue are present in our catalogue. Our catalogue benefits from the use of enhanced station coverage and improved methodology. The total number of events in our catalogue in 2017, 2018, 2019, and 2020 were 62, 47, 9579 and 8220, respectively. The first two years correspond to seismicity in the NMT where poor station coverage makes it difficult to detect small magnitude events. The magnitude of completeness within the KSMMA (ML = ~0.7) is significantly smaller than that obtained for the NMT (ML = ~1.4). The new catalogue is released with separate files for origins, arrivals, and magnitudes which can be joined using the unique ID assigned to each event.
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Bano, Masooda, and Zeena Oberoi. Embedding Innovation in State Systems: Lessons from Pratham in India. Research on Improving Systems of Education (RISE), December 2020. http://dx.doi.org/10.35489/bsg-rise-wp_2020/058.

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The learning crisis in many developing countries has led to searches for innovative teaching models. Adoption of innovation, however, disrupts routine and breaks institutional inertia, requiring government employees to change their way of working. Introducing and embedding innovative methods for improving learning outcomes within state institutions is thus a major challenge. For NGO-led innovation to have largescale impact, we need to understand: (1) what factors facilitate its adoption by senior bureaucracy and political elites; and (2) how to incentivise district-level field staff and school principals and teachers, who have to change their ways of working, to implement the innovation? This paper presents an ethnographic study of Pratham, one of the most influential NGOs in the domain of education in India today, which has attracted growing attention for introducing an innovative teaching methodology— Teaching at the Right Level (TaRL) – with evidence of improved learning outcomes among primary-school students and adoption by a number of states in India. The case study suggests that while a combination of factors, including evidence of success, ease of method, the presence of a committed bureaucrat, and political opportunity are key to state adoption of an innovation, exposure to ground realities, hand holding and confidence building, informal interactions, provision of new teaching resources, and using existing lines of communication are core to ensuring the co-operation of those responsible for actual implementation. The Pratham case, however, also confirms existing concerns that even when NGO-led innovations are successfully implemented at a large scale, their replication across the state and their sustainability remain a challenge. Embedding good practice takes time; the political commitment leading to adoption of an innovation is often, however, tied to an immediate political opportunity being exploited by the political elites. Thus, when political opportunity rather than a genuine political will creates space for adoption of an innovation, state support for that innovation fades away before the new ways of working can replace the old habits. In contexts where states lack political will to improve learning outcomes, NGOs can only hope to make systematic change in state systems if, as in the case of Pratham, they operate as semi-social movements with large cadres of volunteers. The network of volunteers enables them to slow down and pick up again in response to changing political contexts, instead of quitting when state actors withdraw. Involving the community itself does not automatically lead to greater political accountability. Time-bound donor-funded NGO projects aiming to introduce innovation, however large in scale, simply cannot succeed in bringing about systematic change, because embedding change in state institutions lacking political will requires years of sustained engagement.
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