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 Hausdorff locally compact space, which possesses 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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I want to express my sincere gratitude for the anonymous referee’s valuable feedback and suggestions on improving the exposition and readability of the manuscript.
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Stefano Ciaci wrote the manuscript in its entirety.
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This work was supported by the Estonian Research Council grants (PSG487) and (PRG1901).
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Ciaci, S. On the Transfinite Symmetric Strong Diameter Two Property. Mediterr. J. Math. 20, 281 (2023). https://doi.org/10.1007/s00009-023-02483-2
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DOI: https://doi.org/10.1007/s00009-023-02483-2