A Fredholm Operator Approach To Morita Equivalence

Ruy Exel

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A Fredholm Operator Approach To Morita Equivalence

Ruy Exel

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Abstract

Given C*-algebras A and B and an imprimitivity A-B-bimodule X, we construct an explicit isomorphism X_* : K_i(A) --> K_i(B) where K_i denote the complex K-theory functors for i=0, 1. Our techniques do not require separability nor existence of countable approximate identities. We thus extend, to general C*-algebras, the result of Brown, Green and Rieffel according to which strongly Morita equivalent C*-algebras have isomorphic K-groups. The method employed includes a study of Fredholm operators on Hilbert modules.

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Ruy Exel. 1992-12-31. A Fredholm Operator Approach To Morita Equivalence. https://arxiv.org/abs/funct-an/9212005

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