K-theory of group Banach algebras and Banach property RD

Original · EN

We investigate Banach algebras of convolution operators on the Lᵖ 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.