Persistence approximation property for \(L^p\) operator algebras

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 \(L^{p}\)...

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Bibliographic Details
Published inarXiv.org
Main Authors Wang, Hang, Wang, Yanru, Zhang, Jianguo, Zhou, Dapeng
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 20.05.2024
Subjects
Algebra
Approximation
Mathematical analysis
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Summary: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.
ISSN:2331-8422