kk-theory for Banach algebras. I: The non-equivariant case

DOI10.1016/j.jfa.2015.03.009zbMath1316.19007arXiv1406.2094OpenAlexW1964827835MaRDI QIDQ2345410

Walther Paravicini

Publication date: 22 May 2015

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.2094

zbMATH Keywords

Banach algebraMorita equivalencehomology theorybivariant \(K\)-theoryKasparov theoryquasi-homomorphism

Mathematics Subject Classification ID

Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) (46M20) Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.) (46M18) Kasparov theory ((KK)-theory) (19K35) Topological algebras, normed rings and algebras, Banach algebras (46H99)

Related Items (1)

\(kk\)-theory for Banach algebras. II: Equivariance and Green-Julg type theorems

Cites Work

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• Algebraic \(K\)-theory and locally convex algebras
• Topological and bivariant K-theory
• Algebraic \(K\)-theory of stable \(C^*\)-algebras
• A new look at KK-theory
• Topological methods for \(C^*\)-algebras. III: Axiomatic homology
• Bivariant \(K\)-theory for locally convex algebras and the Chern-Connes character
• Bivariant \(K\)-theory for Banach algebras and the Baum-Connes conjecture
• A generalised Green-Julg theorem for proper groupoids and Banach algebras
• Categories of fractions and excision in KK-theory
• Triangulated Categories
• THE OPERATORK-FUNCTOR AND EXTENSIONS OFC*-ALGEBRAS
• Morita equivalences and KK-theory for Banach algebras

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