$p$-nuclearity of $L^p$-operator crossed products
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913608541143040 |
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| author | Wang, Zhen Zhu, Sen |
| author_facet | Wang, Zhen Zhu, Sen |
| contents | Let $(X,\mathcal{B},μ)$ be a measure space and $A$ be a norm closed subalgebra of $\mathcal{B}(L^p(X,μ))$, where $p\in [1,\infty)$. 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.} |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_03933 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $p$-nuclearity of $L^p$-operator crossed products Wang, Zhen Zhu, Sen Functional Analysis Operator Algebras Let $(X,\mathcal{B},μ)$ be a measure space and $A$ be a norm closed subalgebra of $\mathcal{B}(L^p(X,μ))$, where $p\in [1,\infty)$. 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.} |
| title | $p$-nuclearity of $L^p$-operator crossed products |
| topic | Functional Analysis Operator Algebras |
| url | https://arxiv.org/abs/2305.03933 |