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arXiv · 2302.14414

On the transfinite symmetric strong diameter two property

Stefano Ciaci
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Abstract

We study transfinite analogues of the symmetric strong diameter two property. We investigate the stability of these properties under $c_0$, $\ell_\infty$ sums and under projective tensor products. Moreover, we characterize Banach spaces of the form $C_0(X)$, where $X$ is a T$_4$ locally compact space, which posses these transfinite properties via cardinal functions over $X$. As an application, we are able to produce a variety of examples of Banach spaces which enjoy or fail these properties.

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Stefano Ciaci. 2023-02-28. On the transfinite symmetric strong diameter two property. https://arxiv.org/abs/2302.14414

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