Categories of operator modules (Morita equivalence and projective modules)

DOI10.1090/memo/0681zbMath0966.46033OpenAlexW1966170307MaRDI QIDQ4950521

Paul S. Muhly, David P. Blecher, Vern I. Paulsen

Publication date: 5 April 2000

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/memo/0681

zbMATH Keywords

completely boundedcategoryoperator spaceHaagerup tensor productprojective moduleoperator algebraMorita equivalencelinking algebraC*-algebrabimodulecomplete isometryimprimitivitycomplete contractivitydual approximate identityduality of operator bimodulesG. Mackey's virtual groupsMorita ring theoryoperator space projective tensor product normstable isomorphism theorem

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) (C^*)-modules (46L08) Abstract operator algebras on Hilbert spaces (47L30) Operator spaces and completely bounded maps (46L07) Projective and injective objects in functional analysis (46M10) Operator spaces (= matricially normed spaces) (47L25) Tensor products of (C^*)-algebras (46L06) Representations of (nonselfadjoint) operator algebras (47L55)

Related Items (41)

Exact structures for operator modules ⋮ Rigged modules. I: Modules over dual operator algebras and the Picard group ⋮ A Morita characterisation for algebras and spaces of operators on Hilbert spaces ⋮ Isomorphisms of function modules, and generalized approximation in modulus ⋮ Limitations on the extendibility of the Radon-Nikodym Theorem ⋮ Nonunital spectral triples and metric completeness in unbounded \(KK\)-theory ⋮ The Fourier algebra of a measured groupoid and its multipliers ⋮ Strong Morita equivalence of operator spaces ⋮ One-sided ideals and approximate identities in operator algebras ⋮ A completely bounded characterization of operator algebras ⋮ Tensorial function theory: from Berezin transforms to Taylor's Taylor series and back ⋮ Unbounded operator algebras ⋮ Morita embeddings for dual operator algebras and dual operator spaces ⋮ Morita equivalence of \(C^*\)-correspondences passes to the related operator algebras ⋮ Hilbert modules, rigged modules, and stable isomorphism ⋮ Morita isomorphism for Cuntz algebras ⋮ A Serre-Swan theorem for bundles of bounded geometry ⋮ Inductive limits in the operator system and related categories ⋮ \(C^\ast\)-algebras and equivalences for \(C^\ast\)-correspondences ⋮ Modules over operator algebras, and the maximal \(C^*\)-dilation ⋮ On stable maps of operator algebras ⋮ Morita equivalence of dual operator algebras ⋮ A Morita type equivalence for dual operator algebras ⋮ A Morita theorem for algebras of operators on Hilbert space ⋮ Stably isomorphic dual operator algebras ⋮ Duality and operator algebras. I: Automatic weak\(^{\ast}\) continuity and applications ⋮ The Shilov boundary of an operator space and the characterization theorems ⋮ Fock space techniques in tensor algebras of directed graphs ⋮ Characterization of Morita equivalence pairs of quantales ⋮ Mauldin-Williams graphs, Morita equivalence and isomorphisms ⋮ Cuntz-Pimnser algebras, completely positive maps and Morita equivalence ⋮ Operator algebras for higher rank analysis and their application to factorial languages ⋮ A characterization and a generalization of $W^{*}$-modules ⋮ Relative Yoneda cohomology for operator spaces ⋮ Tensor algebras over \(C^*\)-correspondences: Representations, dilations, and \(C^*\)-envelopes ⋮ A topology for operator modules over \(W^*\)-algebras ⋮ A Morita theorem for dual operator algebras ⋮ Morita equivalence of \(W^{*}\)-correspondences and their Hardy algebras ⋮ Bimodules, spectra, and Fell bundles ⋮ Hilbert $C^*$-modules over $\varSigma ^*$-algebras ⋮ Stable isomorphism of dual operator spaces

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