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Morita equivalences and KK-theory for Banach algebras

Part of: Modules, bimodules and ideals Selfadjoint operator algebras $K$-theory and operator algebras

Published online by Cambridge University Press:  15 December 2008

Walther Paravicini
Walther Paravicini
Affiliation:
Westfälische Wilhelms–Universität, Einsteinstraβe 62, 48149 Münster, Germany, (w.paravicini@uni-muenster.de).
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Abstract

Vincent Lafforgue's bivariant K-theory for Banach algebras is invariant in the second variable under a rather general notion of Morita equivalence. In particular, the ordinary topological K-theory for Banach algebras is invariant under Morita equivalences.

Keywords

K-theoryMorita equivalenceKKban-theoryequivariantBanach algebra

MSC classification

Secondary: 46L80: $K$-theory and operator algebras (including cyclic theory) 19K35: Kasparov theory ($KK$-theory) 16D90: Module categories ; module theory in a category-theoretic context; Morita equivalence and duality
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 8 , Issue 3 , July 2009 , pp. 565 - 593
Copyright
Copyright © Cambridge University Press 2008

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References

1.Echterhoff, S., Kaliszewski, S., Quigg, J. and Raeburn, I., A categorical approach to imprimitivity theorems for C*-dynamical systems, Memoirs of the American Mathematical Society, Volume 180 (American Mathematical Society, Providence, RI, 2006).Google Scholar
2.Grønbæk, N., Morita equivalence for Banach algebras, J. Pure Appl. Alg. 99 (1995), 183–219.CrossRefGoogle Scholar
3.Grønbæk, N., Morita equivalence for self-induced Banach algebras, Houston J. Math. 22 (1996), 109–140.Google Scholar
4.Lafforgue, V., K-théorie bivariante pour les algèbres de Banach et conjecture de Baum–Connes, Invent. Math. 149 (2002), 1–95.CrossRefGoogle Scholar
5.Lafforgue, V., Equivalences de Morita entre algèbres de Banach, unpublished note (2004).Google Scholar
6.Lafforgue, V., K-théorie bivariante pour les algèbres de Banach, groupoïdes et conjecture de Baum-Connes. Avec un appendice d'Hervé Oyono-Oyono, J. Inst. Math. Jussieu 6 (2007), 415–451.CrossRefGoogle Scholar
7.Paravicini, W., KK-theory for Banach algebras and proper groupoids, PhD thesis, Universität Münster (2007).Google Scholar
8.Pisier, G., On a question of Grønbæk, Math. Proc. R. Irish Acad. A 100 (2000), 55–58.Google Scholar
9.Raeburn, I. and Williams, D. P., Morita equivalence and continuous-trace C*-algebras, Mathematical Surveys and Monographs, Volume 60 (American Mathematical Society, Providence, RI, 1998).CrossRefGoogle Scholar