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arXiv · 2206.08651

On weak compactness in projective tensor products

José Rodríguez
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Abstract

We study the property of being strongly weakly compactly generated (and some relatives) in projective tensor products of Banach spaces. Our main result is as follows. Let $1<p,q<\infty$ be such that $1/p+1/q\geq 1$. Let $X$ (resp., $Y$) be a Banach space with a countable unconditional finite-dimensional Schauder decomposition having a disjoint lower $p$-estimate (resp., $q$-estimate). If $X$ and $Y$ are strongly weakly compactly generated, then so is its projective tensor product $X \widehat{\otimes}_\pi Y$.

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José Rodríguez. 2022-06-17. On weak compactness in projective tensor products. https://arxiv.org/abs/2206.08651

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