Persistence Approximation Property for Lp Operator Algebras

Citation:

Hang WANG,Yanru WANG,Jianguo ZHANG,Dapeng ZHOU.Persistence Approximation Property for Lp Operator Algebras[J].Chinese Annals of Mathematics B,2024,45(6):869~904
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Authors:

Hang WANG; Yanru WANG;Jianguo ZHANG;Dapeng ZHOU

Foundation:

the National Natural Science Foundation of China (Nos. 12271165, 12171156, 12301154) and the Science and Technology Commission of Shanghai Municipality (No. 22DZ2229014)
Abstract: In this paper, the authors study the persistence approximation property for quantitative K-theory of filtered Lp operator algebras. Moreover, they define quantitative assembly maps for Lp operator algebras when p ∈ [1, ∞). Finally, in the case of Lp crossed products and Lp Roe algebras, sufficient conditions for the persistence approximation property are found. This allows to give some applications involving the Lp (coarse) Baum-Connes conjecture.

Keywords:

Lp operator algebra, Quantitative assembly map, Persistence approximation property, Lp Baum-Connes conjecture

Classification:

46L80, 58B34
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