p-nuclearity of L^p-operator crossed products

2023/05/06 by Zhen Wang, Wang, Zhen, Sen Zhu +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2305.03933

openalex publication_date 2023/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (X,B,μ) be a measure space and A be a norm closed subalgebra of B(L^p(X,μ)), where p∈ [1,∞). Let (G,A,α) be an L^p-operator algebra dynamical system, where G is a countable discrete amenable group. We prove that the full L^p-operator crossed product F^p(G,A,α) is p-nuclear if and only if A is p-nuclear provided the action α of G on A is p-completely isometric. As applications, we prove that L^p-Cuntz algebras and rotation L^p-operator algebras are p-nuclear. Our results solve a problem raised by N. C. Phillips concerning p-nuclearity for L^p-Cuntz algebras.

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