Hilbert \(C^*\) and \(W^*\)-modules and their morphisms
type: Item
instance of: scholarly article
title: Hilbert \(C^*\) and \(W^*\)-modules and their morphisms
zbMATH Open document ID: 0968.46041
DOI: 10.1007/BF02355447
published in: Journal of Mathematical Sciences (New York)
publication date: 2000-08-27T00:00:00Z
review text: The paper is a survey on the theory of Hilbert \(C^\ast\)- and \(W^\ast\)-modules and its applications built on lectures given at the State Univ. of Moscow in 1996. In the first two sections the authors present the original work by W. L. Paschke on Hilbert \(C^\ast\)-modules, and the applications obtained by A. S. Mishchenko and A. T. Fomenko to the index theory of generalized Fredholm operators. In the next section they collect properties of Hilbert \(W^\ast\)-modules, in particular, the characterization of self-dual ones given by M. Frank. In the final section they study reflexive Hilbert \(W^\ast\)-modules, referring to work done by V. A. Trofimov and conclude with some of their own results on conditional expectations obtained in joint work with M. Frank.
Mathematics Subject Classification ID: 46L08
zbMATH DE Number: 1495334
zbMATH Keywords: Hilbert \(C^\ast\)-modules
author: Vladimir M. Manuilov
author: E. V. Troitskij
MaRDI profile type: Publication
cites work: On the eigenvalues of the perturbed Schrödinger operator with irrational magnetic flow
cites work: Q4040649
cites work: On approximate factorizations of completely positive maps
cites work: Q3344718
cites work: \(C^*\)-algèbres de Hopf et théorie de Kasparov équivariante. (Hopf \(C^*\)-algebras and equivariant Kasparov theory)
cites work: Q3805292
cites work: Q3730469
cites work: A new approach to Hilbert \(C^*\)-modules
cites work: A generalization of Hilbert modules
cites work: Correction
cites work: Stable isomorphism of hereditary subalgebras of \(C^*\)-algebras
cites work: Stable isomorphism and strong Morita equivalence of \(C^*\)-algebras
cites work: Q4310044
cites work: A survey of some aspects of non-commutative geometry
cites work: Q5531996
cites work: Q5565478
cites work: Champs continus d'espaces hilbertiens et de $C^*$-algèbres
cites work: Q3930236
cites work: Embedding AW∗ -Algebras as Double Commutants in Type I Algebras
cites work: Self-duality and \(C^*\)-reflexivity of Hilbert \(C^*\)-moduli
cites work: On conditional expectations arising from group actions
cites work: Lefschetz numbers and geometry of operators in \(W^*\)-modules
cites work: On a new topology in the space of Fredholm operators
cites work: Centralisers and Operators Reduced By Maximal Ideals
cites work: Q4359479
cites work: Modules Over Operator Algebras
cites work: Q4160083
cites work: Q4094170
cites work: Q3894484
cites work: Q3905956
cites work: Q3139069
cites work: Q3034367
cites work: On nuclear C\(^*\)-algebras
cites work: Q4328332
cites work: Rieffel induction as generalized quantum Marsden-Weinstein reduction
cites work: Q5287648
cites work: Injective Hilbert \(C^*\)-modules
cites work: Hilbert 𝐶*-modules in which all closed submodules are complemented
cites work: Diagonalization of compact operators in Hilbert modules over finite \(W^*\)-algebras
cites work: On the contractability of the unitary group of the Hilbert space over a C*-algebra
cites work: Equivariant Triviality Theorems for Hilbert C ∗ -Modules
cites work: Q3869837
cites work: Q3675001
cites work: Q3205823
cites work: Cohomology of topological groups and solvmanifolds
cites work: Q3997462
cites work: On rings of operators
cites work: Inner Product Modules Over B ∗ -Algebras
cites work: The Double B-Dual Of An Inner Product Module Over a C*-Algebra B
cites work: Integrable group actions on von Neumann algebras.
cites work: Q3205815
cites work: Induced representations of C\(^*\)-algebras
cites work: Morita equivalence for C\(^*\)-algebras and W\(^*\)-algebras
cites work: Strong Morita equivalence of certain transformation group \(C^*\)-algebras
cites work: Q5667036
cites work: Q5624220
cites work: Q4507229
cites work: Theory of operator algebras I.
cites work: Reflexivity of Hilbertian modules over the algebra of compact operators with an adjoint unit
cites work: Reflexive and self-dual Hilbert modules over certainC*-algebras
cites work: Contractibility of the full general linear group of the \(C^ *\)-Hilbert module \(\ell _ 2(A)\)
cites work: Q4956094
cites work: Geometry and topology of operators on Hilbert \(C^*\)-modules
cites work: Index for 𝐶*-subalgebras
cites work: Unbounded elements affiliated with \(C^*\)-algebras and non-compact quantum groups
cites work: Operator theory in the \(C^*\)-algebra framework

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