$p$-nuclearity of reduced group $L^p$-operator algebras

Zhen Wang

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arXiv · 2412.18643

$p$-nuclearity of reduced group $L^p$-operator algebras

Zhen Wang

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Abstract

Let $p\in (1,\infty)$ and let $G$ be a discrete group. G. An, J.-J. Lee and Z.-J. Ruan introduced $p$-nuclearity for $L^p$-operator algebras. They proved that the reduced group $L^p$-operator algebra $F^p_\lambda(G)$ is $p$-nuclear if $G$ is amenable. In this paper, we show that the converse is true. This answers an open problem concerning the $p$-nuclearity for reduced group $L^p$-operator algebras of N. C. Phillips.

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Zhen Wang. 2024-12-24. $p$-nuclearity of reduced group $L^p$-operator algebras. https://arxiv.org/abs/2412.18643

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