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arXiv · 2211.12262

Persistence approximation property for $L^p$ operator algebras

Hang Wang·Yanru Wang·Jianguo Zhang·Dapeng Zhou
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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.

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Hang Wang, Yanru Wang, Jianguo Zhang, Dapeng Zhou. 2022-11-22. Persistence approximation property for $L^p$ operator algebras. https://doi.org/10.1007/s11401-024-0043-3

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