Relevant bibliographies by topics / Banach algebra

Academic literature on the topic 'Banach algebra'

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Published: 4 June 2021
Last updated: 3 March 2023

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Journal articles on the topic "Banach algebra"

1

Miller, John Boris. "Strictly real Banach algebras." Bulletin of the Australian Mathematical Society 47, no. 3 (June 1993): 505–19. http://dx.doi.org/10.1017/s000497270001532x.

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A complex Banach algebra is a complexification of a real Banach algebra if and only if it carries a conjugation operator. We prove a uniqueness theorem concerning strictly real selfconjugate subalgebras of a given complex algebra. An example is given of a complex Banach algebra carrying two distinct but commuting conjugations, whose selfconjugate subalgebras are both strictly real. The class of strictly real Banach algebras is shown to be a variety, and the manner of their generation by suitable elements is proved. A corollary describes some strictly real subalgebras in Hermitian Banach star algebras, including C* algebras.
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Gourdeau, Frédéric. "Amenability of Lipschitz algebras." Mathematical Proceedings of the Cambridge Philosophical Society 112, no. 3 (November 1992): 581–88. http://dx.doi.org/10.1017/s0305004100071267.

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In this article, we study the amenability of Banach algebras in general, and that of Lipschitz algebras in particular. After introducing an alternative definition of amenability, we extend a result of [5], thereby proving a new characterization of amenability for Banach algebras. This characterization relates the amenability of a Banach algebra A to the space of bounded homomorphisms from A into another Banach algebra B (Theorem 4). This result allows us to solve the problem of amenability for virtually all Lipschitz algebras (of complex or Banach algebra valued functions), a class of algebras which has been studied in [2], [4] and [5].
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Khodakarami, Wania, Hoger Ghahramani, and Esmaeil Feizi. "Relative amenability of Banach algebras." Filomat 36, no. 6 (2022): 2091–103. http://dx.doi.org/10.2298/fil2206091k.

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Let A be a Banach algebra and I be a closed ideal of A. We say that A is amenable relative to I, if A/I is an amenable Banach algebra. We study the relative amenability of Banach algebras and investigate the relative amenability of triangular Banach algebras and Banach algebras associated to locally compact groups. We generalize some of the previous known results by applying the concept of relative amenability of Banach algebras, especially, we present a generalization of Johnson?s theorem in the concept of relative amenability.
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ABTAHI, F., and A. GHAFARPANAH. "A NOTE ON CYCLIC AMENABILITY OF THE LAU PRODUCT OF BANACH ALGEBRAS DEFINED BY A BANACH ALGEBRA MORPHISM." Bulletin of the Australian Mathematical Society 92, no. 2 (June 16, 2015): 282–89. http://dx.doi.org/10.1017/s0004972715000544.

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Let $T$ be a Banach algebra homomorphism from a Banach algebra ${\mathcal{B}}$ to a Banach algebra ${\mathcal{A}}$ with $\Vert T\Vert \leq 1$. Recently, Bhatt and Dabhi [‘Arens regularity and amenability of Lau product of Banach algebras defined by a Banach algebra morphism’, Bull. Aust. Math. Soc.87 (2013), 195–206] showed that cyclic amenability of ${\mathcal{A}}\times _{T}{\mathcal{B}}$ is stable with respect to $T$, for the case where ${\mathcal{A}}$ is commutative. In this note, we address a gap in the proof of this stability result and extend it to an arbitrary Banach algebra ${\mathcal{A}}$.
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Lee, Yang-Hi. "Stability of -Jordan Homomorphisms from a Normed Algebra to a Banach Algebra." Abstract and Applied Analysis 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/691025.

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We establish the hyperstability of -Jordan homomorphisms from a normed algebra to a Banach algebra, and also we show that an -Jordan homomorphism between two commutative Banach algebras is an -ring homomorphism.
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MONFARED, MEHDI SANGANI. "Character amenability of Banach algebras." Mathematical Proceedings of the Cambridge Philosophical Society 144, no. 3 (May 2008): 697–706. http://dx.doi.org/10.1017/s0305004108001126.

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AbstractWe introduce the notion of character amenable Banach algebras. We prove that character amenability for either of the group algebra L1(G) or the Fourier algebra A(G) is equivalent to the amenability of the underlying group G. Character amenability of the measure algebra M(G) is shown to be equivalent to G being a discrete amenable group. We also study functorial properties of character amenability. For a commutative character amenable Banach algebra A, we prove all cohomological groups with coefficients in finite-dimensional Banach A-bimodules, vanish. As a corollary we conclude that all finite-dimensional extensions of commutative character amenable Banach algebras split strongly.
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Yost, David. "Strictly Convex Banach Algebras." Axioms 10, no. 3 (September 11, 2021): 221. http://dx.doi.org/10.3390/axioms10030221.

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We discuss two facets of the interaction between geometry and algebra in Banach algebras. In the class of unital Banach algebras, there is essentially one known example which is also strictly convex as a Banach space. We recall this example, which is finite-dimensional, and consider the open question of generalising it to infinite dimensions. In C∗-algebras, we exhibit one striking example of the tighter relationship that exists between algebra and geometry there.
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LIU, CHENG–KAI. "The structure of triple homomorphisms onto prime algebras." Mathematical Proceedings of the Cambridge Philosophical Society 168, no. 2 (October 23, 2018): 345–60. http://dx.doi.org/10.1017/s0305004118000737.

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AbstractTriple homomorphisms on C*-algebras and JB*-triples have been studied in the literature. From the viewpoint of associative algebras, we characterise the structure of triple homomorphisms from an arbitrary ⋆-algebra onto a prime *-algebra. As an application, we prove that every triple homomorphism from a Banach ⋆-algebra onto a prime semisimple idempotent Banach *-algebra is continuous. The analogous results for prime C*-algebras and standard operator *-algebras on Hilbert spaces are also described.
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Ludkovsky, S., and B. Diarra. "Spectral integration and spectral theory for non-Archimedean Banach spaces." International Journal of Mathematics and Mathematical Sciences 31, no. 7 (2002): 421–42. http://dx.doi.org/10.1155/s016117120201150x.

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Banach algebras over arbitrary complete non-Archimedean fields are considered such that operators may be nonanalytic. There are different types of Banach spaces over non-Archimedean fields. We have determined the spectrum of some closed commutative subalgebras of the Banach algebraℒ(E)of the continuous linear operators on a free Banach spaceEgenerated by projectors. We investigate the spectral integration of non-Archimedean Banach algebras. We define a spectral measure and prove several properties. We prove the non-Archimedean analog of Stone theorem. It also contains the case ofC-algebrasC∞(X,𝕂). We prove a particular case of a representation of aC-algebra with the help of aL(Aˆ,μ,𝕂)-projection-valued measure. We consider spectral theorems for operators and families of commuting linear continuous operators on the non-Archimedean Banach space.
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Garimella, Ramesh V. "On continuity of derivations and epimorphisms on some vector-valued group algebras." Bulletin of the Australian Mathematical Society 56, no. 2 (October 1997): 209–15. http://dx.doi.org/10.1017/s0004972700030938.

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For a locally compact Abelian group G and a commutative Banach algebra B, let L1(G, B) be the Banach algebra of all Bochner integrable functions. We show that if G is compact and B is a nonunital Banach algebra without nontrivial zero divisors, then (i) all derivations on L1(G, B) are continuous if and only if all derivations on B are continuous, and (ii) each epimorphism from a Banach algebra X onto L1(G, B) is continuous provided every epimorphism from X onto B is continuous. If G is noncompact then every derivation on L1(G, B) and every epimorphism from a commutative Banach algebra onto L1(G, B) are continuous. Our results extend the results of Neumann and Velasco for nonunital Banach algebras.
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Dissertations / Theses on the topic "Banach algebra"

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Mudau, Leonard Gumani. "Zero divisors in banach algebras." Thesis, University of Limpopo (Medunsa Campus), 2010. http://hdl.handle.net/10386/632.

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Yang, Hongfei. "Properties of Banach function algebras." Thesis, University of Nottingham, 2018. http://eprints.nottingham.ac.uk/49075/.

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This thesis is devoted to the study of various properties of Banach function algebras. We are particularly interested in the study of antisymmetric decompositions for uniform algebras and regularity of Banach function algebras. We are also interested in the study of Swiss cheese sets, essential uniform algebras and characterisations of C(X) among its subalgebras. The maximal antisymmetric decomposition for uniform algebras is a generalisation of the celebrated Stone-Weierstrass theorem and it is a powerful tool in the study of uniform algebras. However, in the literature, not much attention has been paid to the study of closed antisymmetric subsets. In Section 1.7 we give a characterisation of all the closed antisymmetric subsets for the disc algebra on the unit circle, and we use this characterisation to give a new proof of Wermer’s maximality theorem. Then in Section 4.1 we give characterisations of all the closed antisymmetric subsets for normal uniform algebras on the unit interval or the unit circle. The two types of regularity points, the R-point and the point of regularity, are important concepts in the study of regularity of Banach function algebras. In Section 3.2 we construct two examples of compact plane sets X, such that R(X) has either one R-point while having no points of regularity, or R(X) has one point of continuity while having no R-points. There are the first known examples of natural uniform algebras in the literature which show that R-points and points of continuity can be different. We then use properties of regularity points to study R(X) which is not regular while having no non-trivial Jensen measures. We also use properties of regularity points in Section 4.2 to study small exceptional sets for uniform algebras. In Chapter 2 we study Swiss cheese sets. Our approach is to regard Swiss cheese sets “abstractly”: we study the family of sequences of pairs of numbers, where the numbers represent the centre and radius of discs in the complex plane. We then give a natural topology on the space of abstract Swiss cheeses and give topological proofs of various classicalisation theorems. It is standard that the study of general uniform algebras can be reduced to the study of essential uniform algebras. In Chapter 5 we study methods to construct essential uniform algebras. In particular, we continue to study the method introduced in [26] to show that some more properties are inherited by the constructed essential uniform algebra from the original one. We note that the material in Chapter 2 is joint work with J. Feinstein and S. Morley and is published in [28, 27]. The material in Chapter 3 is joint work with J. Feinstein and is published in [32]. Section 4.2 contains joint work with J. Feinstein.
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Esslamzadeh, Gholam Hossein. "Banach algebra structure and amenability of a class of matrix algebras with applications." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0002/NQ29033.pdf.

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Knapper, Andrew. "Derivations on certain banach algebras." Thesis, University of Birmingham, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.368411.

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Das, Bata Krishna. "Quantum stochastic analysis in Banach space and operator space." Thesis, Lancaster University, 2012. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.660115.

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Seidel, Markus. "On some Banach Algebra Tools in Operator Theory." Doctoral thesis, Universitätsbibliothek Chemnitz, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-83750.

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Die vorliegende Arbeit ist der Untersuchung von Operatorfolgen gewidmet, die typischerweise bei der Anwendung von Approximationsverfahren auf stetige lineare Operatoren entstehen. Dabei stehen die Stabilität der Folgen sowie das asymptotische Verhalten gewisser Charakteristika wie Normen, Konditionszahlen, Fredholmeigenschaften und Pseudospektren im Mittelpunkt. Das Hauptaugenmerk liegt auf der Entwicklung der Theorie für Operatoren auf Banachräumen. Hierbei bildet ein dafür geeigneter Konvergenzbegriff, die sogenannte P-starke Konvergenz, den Ausgangspunkt, welcher das Studium der gewünschten Eigenschaften in einer erstaunlichen Allgemeinheit gestattet. Die erzielten Resultate kommen, neben einer Reihe weiterer Anwendungen, insbesondere für das Projektionsverfahren für banddominierte Operatoren zum Einsatz.
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Boos, Lynette J. "Function Algebras on Riemann Surfaces and Banach Spaces." Bowling Green State University / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1151340555.

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Wimelaratna, Ramasinghege. "Multi dimensional geometric moduli and exterior algebra of a Banach space /." The Ohio State University, 1988. http://rave.ohiolink.edu/etdc/view?acc_num=osu148759830383865.

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Calzi, Mattia. "Functional Calculus on Homogeneous Groups." Doctoral thesis, Scuola Normale Superiore, 2019. http://hdl.handle.net/11384/85740.

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In the first part of the thesis, we consider the following problem. Let G be a homogeneous group, and let (L_1,...,L_n) be a jointly hypoelliptic commutative finite family of formally self-adjoint, homogeneous, left-invariant differential operators without constant terms. Then, the operators L_j are essentially self-adjoint as operators on L^2(G) with domain C^infty_c(G), and their closures commute emph{as self-adjoint operators}. Therefore, one may consider the joint functional calculus associated with the family (L_1,...,L_n). More precisely, for every bounded Borel measurable function $m$ on $R^n$, the corresponding operator m(L_1,...,L_n) commutes with left translations, so that it admits a unique right convolution kernel K(m). The so-defined kernel transform K then maps S(R^n) continuously into S(G), and L^2(eta) isometrically into L^2(G) for some uniquely determined positive Radon measure eta on R^n; this latter property can be considered as an analogue of the Plancherel isomorphism. In addition, K maps L^1(eta) continuously into C_0(G), and this property can be considered as an analogue of the Riemann--Lebesgue lemma. We focus on the following properties of K: (RL) if K(m)in L^1(G), then m can be taken in C_0(R^n): this is again an analogue of the Riemann--Lebesgue lemma; (S) if K(m)in S(G), then m can be taken in S(R^n). We prove that properties (RL) and (S) are compatible with products, and we characterize the Rockland operators which satisfy property (S) when the underlying group G is abelian. We then consider the case of 2-step stratified groups, and families whose elements are either sub-Laplacians or vector fields of homogeneous degree 2. In this setting, we prove several sufficient conditions, as well as some necessary ones, for properties (RL) and (S); we even characterize them in some more specific settings. In addition, we study the case of general (that is, not necessarily homogeneous) sub-Laplacians on 2-step stratified groups, and prove that they always satisfy properties (RL) and (S). We also prove that, under some mild assumptions, a multiplier m can be taken so as to satisfy Mihlin--Hormander conditions of order infinity if and only if the corresponding kernel K(m) satisfies Calderon--Zygmund conditions of order infinity. In the second part of the thesis, we present some results which are joint work with T. Bruno. We fix the standard sub-Laplacian on an H-type group, and consider its heat kernel (p_s)_{s>0}. We provide sharp asymptotic estimates at $infty$ for basically all the derivatives of p_1. Because of the homogeneity of the family (p_s), these estimates can also be considered as short-time asymptotics.
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Mendoza, Quispe Wilfredo. "K-teoría de C*-álgebras." Master's thesis, Universidad Nacional Mayor de San Marcos, 2014. https://hdl.handle.net/20.500.12672/3780.

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El objetivo principal de esta tesis es calcular la K-Teoría de las C∗-Álgebras y con aplicación al cálculo de la K-Teoría del Álgebra de Cuntz y Álgebra de Toeplitz mediante la K-teoría de las C∗-Álgebras de grafos dirigidos.
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Books on the topic "Banach algebra"

1

Harmand, P. M-ideals in Banach spaces and Banach algebras. Berlin: Springer-Verlag, 1993.

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A course in commutative Banach algebras. New York, NY: Springer, 2009.

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Kaniuth, Eberhard. A course in commutative Banach algebras. New York, NY: Springer, 2009.

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Palmer, Theodore W. Banach algebras and the general theory of *-algebras. Cambridge [England]: Cambridge University Press, 1994.

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Palmer, Theodore W. Banach algebras and the general theory of *-algebras. Cambridge: Cambridge University Press, 2001.

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García, Miguel Cabrera. Non-associative normed algebras. Cambridge: Cambridge University Press, 2014.

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Bade, W. G. Algebraic and strong splittings of extensions of Banach algebras. Providence, R.I: American Mathematical Society, 1999.

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Gelʹfand, I. M. Commutative normed rings. Providence, RI: AMS Chelsea Publishing, 2003.

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Gelʹfand, I. M. Commutative normed rings. Providence, RI: AMS Chelsea Publishing, 2003.

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Gelʹfand, I. M. Commutative normed rings. Providence, RI: American Mathematical Society, 1999.

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Book chapters on the topic "Banach algebra"

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Runde, Volker. "Banach Homological Algebra." In Springer Monographs in Mathematics, 259–83. New York, NY: Springer New York, 2020. http://dx.doi.org/10.1007/978-1-0716-0351-2_6.

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Mortini, Raymond, and Rudolf Rupp. "Banach algebra techniques." In Extension Problems and Stable Ranks, 375–671. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-73872-3_7.

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Rosenthal, Haskell. "The lie algebra of a Banach space." In Banach Spaces, 129–57. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/bfb0074702.

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Queffélec, Martine. "The Banach Algebra M(T)." In Substitution Dynamical Systems - Spectral Analysis, 1–19. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11212-6_1.

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Howie, John, Steven Duplij, Ali Mostafazadeh, Masaki Yasue, and Vladimir Ivashchuk. "Infinite-Dimensional Grassmann-Banach Algebra." In Concise Encyclopedia of Supersymmetry, 201. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/1-4020-4522-0_264.

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Garcia, Miguel Cabrera, Antonio Moreno Galindo, and Angel Rodriguez Palacios. "On Primitive Jordan Banach Algebras." In Non-Associative Algebra and Its Applications, 54–59. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-0990-1_9.

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Berkovich, Vladimir. "The dimension of a Banach algebra." In Mathematical Surveys and Monographs, 153–59. Providence, Rhode Island: American Mathematical Society, 2012. http://dx.doi.org/10.1090/surv/033/10.

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Sahebi, Shervin, and Venus Rahmani. "Generalized Derivations on Rings and Banach Algebras." In Algebra and its Applications, 81–87. Singapore: Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-1651-6_6.

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Ashraf, Mohammad, and Bilal Ahmad Wani. "On Commutativity of Banach $$^*$$ ∗ -Algebras with Derivation." In Homological and Combinatorial Methods in Algebra, 27–39. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74195-6_3.

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Garcia, Miguel Cabrera, and Angel Rodriguez Palacios. "Zel’Manov’s Theorem for Nondegenerately Ultraprime Jordan-Banach Algebras." In Non-Associative Algebra and Its Applications, 60–65. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-0990-1_10.

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Conference papers on the topic "Banach algebra"

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Laustsen, Niels Jakob, and Richard J. Loy. "Closed ideals in the Banach algebra of operators on a Banach space." In Topological Algebras, their Applications, and Related Topics. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2005. http://dx.doi.org/10.4064/bc67-0-20.

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PLAKSA, S. A. "AN INFINITE-DIMENSIONAL COMMUTATIVE BANACH ALGEBRA AND SPATIAL POTENTIAL FIELDS." In Proceedings of the 6th International ISAAC Congress. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812837332_0021.

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Armǎşelu, Anca, Nicolae Tiţa, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Hereditary Properties of Some Bilinear Operators on a Banach Algebra." In ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010. AIP, 2010. http://dx.doi.org/10.1063/1.3498505.

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Wshayeh, Huda A. A., and Boushra Y. Hussein. "On δ-characterization in symmetric Δ-Banach algebra with Hermitian properties." In 3RD INTERNATIONAL SCIENTIFIC CONFERENCE OF ALKAFEEL UNIVERSITY (ISCKU 2021). AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0066889.

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Rakovic, Sasa V. "Minkowski algebra and Banach Contraction Principle in set invariance for linear discrete time systems." In 2007 46th IEEE Conference on Decision and Control. IEEE, 2007. http://dx.doi.org/10.1109/cdc.2007.4434105.

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Hussein, Boushra Y., and Huda A. A. Wshayeh. "On state space of measurable function in symmetric Δ-Banach algebra with new results." In PROCEEDING OF THE 1ST INTERNATIONAL CONFERENCE ON ADVANCED RESEARCH IN PURE AND APPLIED SCIENCE (ICARPAS2021): Third Annual Conference of Al-Muthanna University/College of Science. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0093486.

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Kravtsiv, Viktoriia, and Diana Vitrykus. "Generating elements of the algebra of block-symmetric polynomials on the product of Banach spaces ℂs." In 10TH INTERNATIONAL CONFERENCE ON APPLIED SCIENCE AND TECHNOLOGY. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0115680.

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Jarosz, Krzysztof. "Wiesław Żelazko, topological algebras, Banach algebras." In Topological Algebras, their Applications, and Related Topics. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2005. http://dx.doi.org/10.4064/bc67-0-1.

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BASSEY, U. N. "ON COMPACT ELEMENTS OF BANACH ALGEBRAS." In Proceedings of the Fourth International Workshop. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812773241_0020.

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González, Manuel. "Banach spaces with small Calkin algebras." In Perspectives in Operator Theory. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2007. http://dx.doi.org/10.4064/bc75-0-10.

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