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K-theory of group Banach algebras and Banach property RD
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abstract
We investigate Banach algebras of convolution operators on the $L^p$ spaces of a locally compact group, and their K-theory. We show that for a discrete group, the corresponding K-theory groups depend continuously on $p$ in an inductive sense. Via a Banach version of property RD, we show that for a large class of groups, the K-theory groups of the Banach algebras are independent of $p$.
Forward citations
Cited by 3 Pith papers
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Spectral Invariance and Gevrey Regularity for Groups with strongly subexponential growth
Gevrey-Beurling operator algebras inside unitized q-pseudofunction algebras are inverse-closed for unimodular groups of strong subexponential growth, yielding spectral invariance and K-theory isomorphisms.
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On some $p$-approximation properties of exact discrete groups and $\ell^p$ uniform Roe algebras
Proves property A implies p-nuclearity of ℓ^p uniform Roe algebras, introduces p-ITAP for groups, and characterizes exact discrete groups via these algebras with p-operator space coefficients.
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