On the transfinite symmetric strong diameter two property

2023/02/28 by Stefano Ciaci, Ciaci, Stefano
Mathematics · #46B04 #46B20 (Primary) 54A25 (Secondary) #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2302.14414

openalex publication_date 2023/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study transfinite analogues of the symmetric strong diameter two property. We investigate the stability of these properties under c₀, ℓ_∞ sums and under projective tensor products. Moreover, we characterize Banach spaces of the form C₀(X), where X is a T₄ 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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