Persistence Approximation Property for L^p Operator Algebras

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.