Persistence approximation property for $L^p$ operator algebras

Abstract

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

33 pages, to appear in Chinese Ann. Math. Ser. B

References in corpus (7)

• Group algebras acting on $L^p$-spaces
• Representations of $p$-convolution algebras on $L^q$-spaces
• Quotients of Banach algebras acting on $L^p$-spaces
• Rigidity of ${\ell }^p$ Roe-type algebras
• Quantitative $K$-theory for Banach algebras
• A quasi-local characterisation of $L^p$-Roe algebras
• Dynamical Complexity and $K$-Theory of $L^p$ Operator Crossed Products

Cited by in corpus (1)

• $L^p$ coarse Baum-Connes conjecture via $C_0$ coarse geometry