Relevant bibliographies by topics / Hilbert C*-module

Academic literature on the topic 'Hilbert C*-module'

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Published: 4 June 2021
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Journal articles on the topic "Hilbert C*-module"

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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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Murphy, Gerard J. "Positive definite kernels and Hilbert C*-modules." Proceedings of the Edinburgh Mathematical Society 40, no. 2 (June 1997): 367–74. http://dx.doi.org/10.1017/s0013091500023804.

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A theory of positive definite kernels in the context of Hilbert C*-modules is presented. Applications are given, including a representation of a Hilbert C*-module as a concrete space of operators and a construction of the exterior tensor product of two Hilbert C*-modules.
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Rashidi-Kouchi, M., and A. Rahimi. "On controlled frames in Hilbert C∗-modules." International Journal of Wavelets, Multiresolution and Information Processing 15, no. 04 (May 7, 2017): 1750038. http://dx.doi.org/10.1142/s0219691317500382.

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In this paper, we introduce controlled frames in Hilbert [Formula: see text]-modules and we show that they share many useful properties with their corresponding notions in Hilbert space. Next, we give a characterization of controlled frames in Hilbert [Formula: see text]-module. Also multiplier operators for controlled frames in Hilbert [Formula: see text]-modules will be defined and some of its properties will be shown. Finally, we investigate weighted frames in Hilbert [Formula: see text]-modules and verify their relations to controlled frames and multiplier operators.
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Frank, Michael, and Alexander A. Pavlov. "Module weak Banach-Saks and module Schur properties of Hilbert C*-modules." Journal of Operator Theory 70, no. 1 (July 24, 2103): 53–73. http://dx.doi.org/10.7900/jot.2011apr21.1933.

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HAMANA, MASAMICHI. "MODULES OVER MONOTONE COMPLETE C*-ALGEBRAS." International Journal of Mathematics 03, no. 02 (April 1992): 185–204. http://dx.doi.org/10.1142/s0129167x92000059.

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The main result asserts that given two monotone complete C*-algebras A and B, B is faithfully represented as a monotone closed C*-subalgebra of the monotone complete C*-algebra End A(X) consisting of all bounded module endomorphisms of some self-dual Hilbert A-module X if and only if there are sufficiently many normal completely positive maps of B into A. The key to the proof is the fact that each pre-Hilbert A-module can be completed uniquely to a self-dual Hilbert A-module.
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ASADI, M. B., M. FRANK, and Z. HASSANPOUR-YAKHDANI. "FRAME-LESS HILBERT C*-MODULES." Glasgow Mathematical Journal 61, no. 1 (February 7, 2018): 25–31. http://dx.doi.org/10.1017/s0017089518000010.

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AbstractWe show that if A is a compact C*-algebra without identity that has a faithful *-representation in the C*-algebra of all compact operators on a separable Hilbert space and its multiplier algebra admits a minimal central projection p such that pA is infinite-dimensional, then there exists a Hilbert A1-module admitting no frames, where A1 is the unitization of A. In particular, there exists a frame-less Hilbert C*-module over the C*-algebra $K(\ell^2) \dotplus \mathbb{C}I_{\ell^2}$.
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Jiang, Runliang. "The irreducibility of C*-algebras acting on Hilbert C*-modules." Filomat 30, no. 9 (2016): 2425–33. http://dx.doi.org/10.2298/fil1609425j.

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Let B be a C*-algebra, E be a Hilbert B module and L(E) be the set of adjointable operators on E. Let A be a non-zero C*-subalgebra of L(E). In this paper, some new kinds of irreducibilities of A acting on E are introduced, which are all the generalizations of those associated to Hilbert spaces. The difference between these irreducibilities are illustrated by a number of counterexamples. It is concluded that for a full Hilbert B-module, these irreducibilities are all equivalent if and only if the underlying C*-algebra B is isomorphic to the C*-algebra of all compact operators on a Hilbert space.
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Frank, Michael, Alexander S. Mishchenko, and Alexander A. Pavlov. "Orthogonality-preserving, C⁎-conformal and conformal module mappings on Hilbert C⁎-modules." Journal of Functional Analysis 260, no. 2 (January 2011): 327–39. http://dx.doi.org/10.1016/j.jfa.2010.10.009.

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Rashidi-Kouchi, Mehdi, Akbar Nazari, and Massoud Amini. "On stability of g-frames and g-Riesz bases in Hilbert C*-modules." International Journal of Wavelets, Multiresolution and Information Processing 12, no. 06 (November 2014): 1450036. http://dx.doi.org/10.1142/s0219691314500362.

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In this paper, we develop the basic stability theory for g-frames and g-Riesz bases in Hilbert C*-module. Also, we study stability of the dual g-frames in Hilbert C*-module. We extend the Casazza–Christensen perturbation theorem to g-frames in Hilbert C*-module but this is not valid for g-Riesz bases. We prove some characterizations of g-frames and g-Riesz bases in Hilbert C*-module.
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Li, Hanfeng. "A Hilbert C*-module admitting no frames." Bulletin of the London Mathematical Society 42, no. 3 (February 3, 2010): 388–94. http://dx.doi.org/10.1112/blms/bdp109.

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Dissertations / Theses on the topic "Hilbert C*-module"

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Ariyani, Mathematics &amp Statistics Faculty of Science UNSW. "The generalized continuous wavelet transform on Hilbert modules." Publisher:University of New South Wales. Mathematics & Statistics, 2008. http://handle.unsw.edu.au/1959.4/42151.

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The construction of the generalized continuous wavelet transform (GCWT) on Hilbert spaces is a special case of the coherent state transform construction, where the coherent state system arises as an orbit of an admissible vector under a strongly continuous unitary representation of a locally compact group. In this thesis we extend this construction to the setting of Hilbert C*-modules. In particular, we define a coherent state transform and a GCWT on Hilbert modules. This construction gives a reconstruction formula and a resolution of the identity formula analogous to those found in the Hilbert space setting. Moreover, the existing theory of standard normalized tight frames in finite countably generated Hilbert modules can be viewed as a discrete case of this construction We also show that the image space of the coherent state transform on Hilbert module is a reproducing kernel Hilbert module. We discuss the kernel and the intertwining property of the group coherent state transform.
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Wood, Peter John, and drwoood@gmail com. "Wavelets and C*-algebras." Flinders University. Informatics and Engineering, 2003. http://catalogue.flinders.edu.au./local/adt/public/adt-SFU20070619.120926.

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A wavelet is a function which is used to construct a specific type of orthonormal basis. We are interested in using C*-algebras and Hilbert C*-modules to study wavelets. A Hilbert C*-module is a generalisation of a Hilbert space for which the inner product takes its values in a C*-algebra instead of the complex numbers. We study wavelets in an arbitrary Hilbert space and construct some Hilbert C*-modules over a group C*-algebra which will be used to study the properties of wavelets. We study wavelets by constructing Hilbert C*-modules over C*-algebras generated by groups of translations. We shall examine how this construction works in both the Fourier and non-Fourier domains. We also make use of Hilbert C*-modules over the space of essentially bounded functions on tori. We shall use the Hilbert C*-modules mentioned above to study wavelet and scaling filters, the fast wavelet transform, and the cascade algorithm. We shall furthermore use Hilbert C*-modules over matrix C*-algebras to study multiwavelets.
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Gruber, Michael. "Nichtkommutative Blochtheorie." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 1998. http://dx.doi.org/10.18452/14360.

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In der vorliegenden Arbeit "Nichtkommutative Blochtheorie" beschäftigen wir uns mit der Spektraltheorie bestimmter Klassen von Hilbertraumoperatoren, den elliptischen Operatoren auf Darstellungsräumen von Hilbert-C*-Moduln. Die auftretenden C*-Algebren kodieren dabei Symmetrieeigenschaften der entsprechenden Operatoren.Für kommutative Symmetrien ist die Blochtheorie ein geeignetes Hilfsmittel. Wir schildern diese Methode zunächst in einem geometrischen Kontext, der allgemein genug ist, um die bekannten Ergebnisse über die Abwesenheit singulärstetigen Spektrums im Hinblick auf physikalische Anwendungen zu erweitern. Wir lassen uns dann durch eine Neuinterpretation der Blochtheorie aus einem nichtkommutativen Blickwinkel inspirieren zur Entwicklung einer nichtkommutativen Blochtheorie. Dabei werden bestimmte Eigenschaften von C*-Algebren verknüpft mit Eigenschaften des Spektrums elliptischer Operatoren. Diese Blochtheorie für Hilbert-C*-Moduln erlaubt es, verschiedene bekannte Resultate aus dem Bereich kommutativer (diskreter und kontinuierlicher) Geometrien mit nichtkommutativen Symmetrien in einem neuen gemeinsamen Rahmen zusammenzufassen, der Raum läßt für Modelle nichtkommutativer Geometrien mit nichtkommutativen Symmetrien. Wichtigstes Beispiel für die behandelte Klasse von Operatoren in der mathematischen Physik sind die Schrödingeroperatoren mit periodischem Magnetfeld und Potential. Wir ordnen sie in den Rahmen kommutativer und nichtkommutativer Blochtheorie ein und wenden die zuvor bereitgestellten Methoden an.
In this doctoral thesis "Nichtkommutative Blochtheorie'' (non-commutative Bloch theory) we investigate the spectral theory of a certain class of operators on Hilbert space: the elliptic operators associated with representations of Hilbert C*-modules. The C*-algebras that arise encode symmetry properties of the corresponding operators. For commutative symmetries Bloch theory is a proper tool. We describe this method in a geometric context which is general enough to extend known results about absence of singular continuous spectrum in view of physical applications. Then --- inspired by a new interpretation of Bloch theory from a non-commutative point of view --- we develop a non-commutative Bloch theory. Here certain properties of C*-algebras get linked to spectral properties of elliptic operators. This Bloch theory for Hilbert \CS-modules allows to unite, in a new common framework, several known results from the field of commutative (discrete and continuous) geometries having non-commutative symmetries; this leaves ample room for models of non-commutative geometries having non-commutative symmetries. In mathematical physics, the most important example for the class of operators considered is given by the Schrödinger operators with periodic magnetic field and potential. We place them into the framework of commutative and non-commutative Bloch theory and apply the methods developed before.
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Jing, Wu. "FRAMES IN HILBERT C*-MODULES." Doctoral diss., University of Central Florida, 2006. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/3137.

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Since the discovery in the early 1950's, frames have emerged as an important tool in signal processing, image processing, data compression and sampling theory etc. Today, powerful tools from operator theory and Banach space theory are being introduced to the study of frames producing deep results in frame theory. In recent years, many mathematicians generalized the frame theory from Hilbert spaces to Hilbert C*-modules and got significant results which enrich the theory of frames. Also there is growing evidence that Hilbert C*-modules theory and the theory of wavelets and frames are tightly related to each other in many aspects. Both research fields can benefit from achievements of the other field. Our purpose of this dissertation is to work on several basic problems on frames for Hilbert C*-modules. We first give a very useful characterization of modular frames which is easy to be applied. Using this characterization we investigate the modular frames from the operator theory point of view. A condition under which the removal of element from a frame in Hilbert C*-modules leaves a frame or a non-frame set is also given. In contrast to the Hilbert space situation, Riesz bases of Hilbert C*-modules may possess infinitely many alternative duals due to the existence of zero-divisors and not every dual of a Riesz basis is again a Riesz basis. We will present several such examples showing that the duals of Riesz bases in Hilbert $C^*$-modules are much different and more complicated than the Hilbert space cases. A complete characterization of all the dual sequences for a Riesz basis, and a necessary and sufficient condition for a dual sequence of a Riesz basis to be a Riesz basis are also given. In the case that the underlying C*-algebra is a commutative W*-algebra, we prove that the set of the Parseval frame generators for a unitary group can be parameterized by the set of all the unitary operators in the double commutant of the unitary group. Similar result holds for the set of all the general frame generators where the unitary operators are replaced by invertible and adjointable operators. Consequently, the set of all the Parseval frame generators is path-connected. We also prove the existence and uniqueness of the best Parseval multi-frame approximations for multi-frame generators of unitary groups on Hilbert C*-modules when the underlying C*-algebra is commutative. For the dilation results of frames we show that a complete Parseval frame vector for a unitary group on Hilbert C*-module can be dilated to a complete wandering vector. For any dual frame pair in Hilbert C*-modules, we prove that the pair are orthogonal compressions of a Riesz basis and its canonical dual basis for some larger Hilbert C*-module. For the perturbation of frames and Riesz bases in Hilbert C*-modules we prove that the Casazza-Christensen general perturbation theorem for frames in Hilbert spaces remains valid in Hilbert C*-modules. In the Hilbert space setting, under the same perturbation condition, the perturbation of any Riesz basis remains a Riesz basis. However, this no longer holds for Riesz bases in Hilbert C*-modules. We also give a complete characterization on all the Riesz bases for Hilbert C*-modules such that the perturbation (under Casazza-Christensen's perturbation condition) of a Riesz basis still remains a Riesz basis.
Ph.D.
Department of Mathematics
Sciences
Mathematics
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Gebhardt, René. "Unbounded operators on Hilbert C*-modules: graph regular operators." Doctoral thesis, Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-213767.

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Let E and F be Hilbert C*-modules over a C*-algebra A. New classes of (possibly unbounded) operators t: E->F are introduced and investigated - first of all graph regular operators. Instead of the density of the domain D(t) we only assume that t is essentially defined, that is, D(t) has an trivial ortogonal complement. Then t has a well-defined adjoint. We call an essentially defined operator t graph regular if its graph G(t) is orthogonally complemented and orthogonally closed if G(t) coincides with its biorthogonal complement. A theory of these operators and related concepts is developed: polar decomposition, functional calculus. Various characterizations of graph regular operators are given: (a, a_*, b)-transform and bounded transform. A number of examples of graph regular operators are presented (on commutative C*-algebras, a fraction algebra related to the Weyl algebra, Toeplitz algebra, C*-algebra of the Heisenberg group). A new characterization of operators affiliated to a C*-algebra in terms of resolvents is given as well as a Kato-Rellich theorem for affiliated operators. The association relation is introduced and studied as a counter part of graph regularity for concrete C*-algebras.
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Gebhardt, René [Verfasser], Konrad [Akademischer Betreuer] Schmüdgen, Konrad [Gutachter] Schmüdgen, and Evgenij V. [Gutachter] Troitsky. "Unbounded operators on Hilbert C*-modules: graph regular operators / René Gebhardt ; Gutachter: Konrad Schmüdgen, Evgenij V. Troitsky ; Betreuer: Konrad Schmüdgen." Leipzig : Universitätsbibliothek Leipzig, 2016. http://d-nb.info/1240695144/34.

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Clare, Pierre. "C*-modules et opérateurs d'entrelacement associés à la série principale de groupes de Lie semi-simples." Phd thesis, Université d'Orléans, 2009. http://tel.archives-ouvertes.fr/tel-00454669.

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Cette thèse est consacrée à l'étude de la série principale unitaire de certains groupes de Lie semi-simples, du point de vue de la géométrie non-commutative. Pour une famille de sous-groupes paraboliques minimaux de composante de Levi L fixée, nous décrivons la famille des représentations de la série principale unitaire associées au moyen de C*-modules sur C*(L). Cette construction s'inspire de celle des modules d'induction de M. A. Rieffel et nous proposons plusieurs modèles pour les C*-modules obtenus, qui reflètent à ce niveau global les réalisations classiques des représentations de la série principale. En rang réel 1, nous caractérisons certains opérateurs bornés sur ces modules, obtenant ainsi un résultat d'irréductibilité analogue à celui de F. Bruhat dans le cas classique. Nous démontrons ensuite la convergence, sur des sous-modules, d'intégrales d'entrelacement analogues à celles définissant les opérateurs de Knapp et Stein. Ces intégrales peuvent être décomposées en somme d'un opérateur densément défini et vraisemblablement borné, d'un opérateur densément défini et d'un terme résiduel, étudiés séparément. Nous indiquons enfin, dans certains cas particuliers, une procédure de normalisation aboutissant à la construction d'opérateurs d'entrelacement unitaires entre C*-modules. Ces opérateurs manifestent l'action du groupe de Weyl régissant les équivalences entre représentations de la série principale au niveau de la C*-algèbre réduite du groupe.
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Marx, Gregory. "Noncommutative Kernels." Diss., Virginia Tech, 2017. http://hdl.handle.net/10919/78353.

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Positive kernels and their associated reproducing kernel Hilbert spaces have played a key role in the development of complex analysis and Hilbert-space operator theory, and they have recently been extended to the setting of free noncommutative function theory. In this paper, we develop the subject further in a number of directions. We give a characterization of completely positive noncommutative kernels in the setting of Hilbert C*-modules and Hilbert W*-modules. We prove an Arveson-type extension theorem for completely positive noncommutative kernels, and we show that a uniformly bounded noncommutative kernel can be decomposed into a linear combination of completely positive noncommutative kernels.
Ph. D.
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"Hilbert C*-modules." 2000. http://library.cuhk.edu.hk/record=b5890533.

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by Ng Yin Fun.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2000.
Includes bibliographical references (leaves 50-51).
Abstracts in English and Chinese.
Acknowledgments --- p.i
Abstract --- p.ii
Introduction --- p.3
Chapter 1 --- Preliminaries --- p.4
Chapter 1.1 --- Hilbert C*-modules --- p.4
Chapter 2 --- Self-dual Hilbert C*-modules --- p.14
Chapter 2.1 --- Self-duality --- p.14
Chapter 2.2 --- Self-duality and some related concepts --- p.22
Chapter 2.3 --- A criterion of self-duality of HA --- p.23
Chapter 3 --- Hilbert W*-modules --- p.25
Chapter 3.1 --- Extension of the inner product to --- p.25
Chapter 3.2 --- Extension of operators to --- p.33
Chapter 3.3 --- Self-dual Hilbert W*-modules --- p.36
Chapter 3.4 --- Some equivalent conditions for a Hilbert W*-module to be self-dual --- p.43
Bibliography --- p.50
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Hsu, Ming-Hsiu, and 許銘修. "Isometries of real and complex Hilbert C*-modules." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/65738727022766899829.

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博士
國立中山大學
應用數學系研究所
100
Let A and B be real or complex C*-algebras. Let V and W be real or complex (right) full Hilbert C*-modules over A and B, respectively. Let T be a linear bijective map from V onto W. We show the following four statements are equivalent. (a) T is a unitary operator, i.e., there is a ∗-isomorphism α : A → B such that = α(), ∀ x,y∈ V ; (b) T preserves TRO products, i.e., T(x) =Tx, ∀ x,y,z in V ; (c) T is a 2-isometry; (d) T is a complete isometry. Moreover, if A and B are commutative, the four statements are also equivalent to (e) T is a isometry. On the other hand, if V and W are complex Hilbert C*-modules over complex C*-algebras, then T is unitary if and only if it is a module map, i.e., T(xa) = (Tx)α(a), ∀ x ∈ V,a ∈ A.
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Books on the topic "Hilbert C*-module"

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Hilbert C*-modules. Providence, R.I: American Mathematical Society, 2005.

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Lance, E. C. Hilbert C*-modules: A toolkit for operator algebraists. Cambridge: Cambridge University Press, 1995.

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Thomsen, Klaus. Hilbert C[asterisk]-modules, KK-theory and C[asterisk]-extensions. Aarhus: Matematisk Institut, Aarhus Universitet, 1988.

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Book chapters on the topic "Hilbert C*-module"

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Jensen, Kjeld Knudsen, and Klaus Thomsen. "Hilbert C*-Modules." In Elements of KK-Theory, 1–46. Boston, MA: Birkhäuser Boston, 1991. http://dx.doi.org/10.1007/978-1-4612-0449-7_1.

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Schmüdgen, Konrad. "Unbounded operators on Hilbert C*-modules and C*-algebras." In The Diversity and Beauty of Applied Operator Theory, 429–41. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-75996-8_23.

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Schmüdgen, Konrad. "Representations on Rigged Spaces and Hilbert $$C^*$$-Modules." In Graduate Texts in Mathematics, 319–45. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-46366-3_14.

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Kwaśniewski, Bartosz Kosma. "Invitation to Hilbert C*-modules and Morita–Rieffel Equivalence." In Trends in Mathematics, 383–88. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-01156-7_39.

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Sahu, Nabin K., and Ekta Rajput. "An Insight into the Frames in Hilbert $$C^*$$-modules." In Springer Proceedings in Mathematics & Statistics, 581–601. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-33-4646-8_46.

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"Preface." In Hilbert C*-Modules, vii—x. Cambridge University Press, 1995. http://dx.doi.org/10.1017/cbo9780511526206.001.

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"Modules and mappings." In Hilbert C*-Modules, 1–13. Cambridge University Press, 1995. http://dx.doi.org/10.1017/cbo9780511526206.002.

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"Multipliers and morphisms." In Hilbert C*-Modules, 14–20. Cambridge University Press, 1995. http://dx.doi.org/10.1017/cbo9780511526206.003.

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"Projections and unitaries." In Hilbert C*-Modules, 21–30. Cambridge University Press, 1995. http://dx.doi.org/10.1017/cbo9780511526206.004.

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"Tensor products." In Hilbert C*-Modules, 31–44. Cambridge University Press, 1995. http://dx.doi.org/10.1017/cbo9780511526206.005.

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Conference papers on the topic "Hilbert C*-module"

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Xiang-Chun Xiao and Xiao-Ming Zeng. "Some properties of mudular frames in Hilbert C*-Modules." In 2009 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR). IEEE, 2009. http://dx.doi.org/10.1109/icwapr.2009.5207497.

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Szafraniec, Franciszek Hugon. "Murphy's ``Positive definite kernels and Hilbert C*-modules'' reorganized." In Noncommutative Harmonic Analysis with Applications to Probability II. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2010. http://dx.doi.org/10.4064/bc89-0-19.

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Frank, Michael, and David R. Larson. "Modular frames for Hilbert C*-modules and symmetric approximation of frames." In International Symposium on Optical Science and Technology, edited by Akram Aldroubi, Andrew F. Laine, and Michael A. Unser. SPIE, 2000. http://dx.doi.org/10.1117/12.408617.

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Арбузов, Виталий, Vitaliy Arbuzov, Эдуард Арбузов, Eduard Arbuzov, Владимир Бердников, Vladimir Berdnikov, Юрий Дубнищев, et al. "Investigation of convective structures and phase transition induced by non-stationary boundary conditions in a horizontal layer of water." In 29th International Conference on Computer Graphics, Image Processing and Computer Vision, Visualization Systems and the Virtual Environment GraphiCon'2019. Bryansk State Technical University, 2019. http://dx.doi.org/10.30987/graphicon-2019-1-53-57.

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The evolution of convective structures and the phase transition induced by non-stationary boundary conditions in a horizontal water layer bounded by flat heat-exchange surfaces were studied by shear interferometry and numerical simulation methods. Numerical modeling of the temperature field as a field of isotherms in the mode of monotonous cooling of horizontal walls was performed. The problem of fragmentary reconstruction of hilbertograms and shear interferograms images from a numerical model of the isotherm field was solved. The hydrodynamics of convective currents, the coevolution of temperature fields, interference and Hilbert structures have been modeled and studied taking into account the inversion of water density in the vicinity of the isotherm (+4°C), under conditions of phase transition and growth of the ice layer on the lower heat transfer plane. The simulation was performed using a proprietary software package. The relevance of this kind of research is due to the special importance of convection in geodynamics, physics of the atmosphere and the ocean, in hydrodynamic and thermophysical processes associated with the formation and growth of crystals.
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Negrut, Dan, Rajiv Rampalli, Gisli Ottarsson, and Anthony Sajdak. "On the Use of the HHT Method in the Context of Index 3 Differential Algebraic Equations of Multibody Dynamics." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85096.

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The paper presents theoretical and implementation aspects related to a new numerical integrator available in the 2005 version of the MSC.ADAMS/Solver C++. The starting point for the new integrator is the Hilber-Hughes-Taylor method (HHT, also known as α-method) that has been widely used in the finite element community for more than two decades. The method implemented is tailored to answer the challenges posed by the numerical solution of index 3 Differential Algebraic Equations that govern the time evolution of a multi-body system. The proposed integrator was tested with more than 1,600 models prior to its release in the 2005 version of the simulation package MSC.ADAMS. In this paper an all-terrain-vehicle model with flexible chassis is used to prove the good efficiency and accuracy of the method.
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Journal articles
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