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arXiv · 1406.2094

kk-Theory for Banach Algebras I: The Non-Equivariant Case

Walther Paravicini
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Abstract

kk$^{\text{ban}}$ is a bivariant K-theory for Banach algebras that has reasonable homological properties, a product and is Morita invariant in a very general sense. We define it here by a universal property and ensure its existence in a rather abstract manner using triangulated categories. The definition ensures that there is a natural transformation from Lafforgue's theory KK$^{\text{ban}}$ into it so that one can take products of elements in KK$^{\text{ban}}$ that lie in kk$^{\text{ban}}$.

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Walther Paravicini. 2014-06-09. kk-Theory for Banach Algebras I: The Non-Equivariant Case. https://arxiv.org/abs/1406.2094

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