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Induction for Banach Algebras, Groupoids and KKban

Published online by Cambridge University Press:  23 October 2009

Walther Paravicini
Walther Paravicini
Affiliation:
Mathematisches Institut der WWU Münster, Einsteinstr. 62, 48149 Münster, Germany, W.Paravicini@uni-muenster.de
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Abstract

Given two equivalent locally compact Hausdorff groupoids, We prove that the Bost conjecture with Banach algebra coefficients is true for one if and only if it is true for the other. This also holds for the Bost conjecture with C*- coefficients. To show these results, the functoriality of Lafforgue's KK-theory for Banach algebras and groupoids with respect to generalised morphisms of groupoids is established. It is also shown that equivalent groupoids have Morita equivalent L1-algebras (with Banach algebra coefficients).

Keywords

Locally compact groupoidKKban-theoryBanach algebraBaum-Connes conjectureBost conjecture

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Type
Research Article
Information
Journal of K-Theory , Volume 4 , Issue 3 , December 2009 , pp. 405 - 468
Copyright
Copyright © ISOPP 2009

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