Persistence Approximation Property for L ^p Operator Algebras

Abstract

In this paper, the authors study the persistence approximation property for quantitative K-theory of filtered L ^p operator algebras. Moreover, they define quantitative assembly maps for L ^p operator algebras when p ∈ [1, ∞). Finally, in the case of L ^p crossed products and L ^p Roe algebras, sufficient conditions for the persistence approximation property are found. This allows to give some applications involving the L ^p (coarse) Baum-Connes conjecture.

Keywords

L ^p operator algebra / Quantitative assembly map / Persistence approximation property / L ^p Baum-Connes conjecture