On the transfinite symmetric strong diameter two property

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.