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 $c_0$, ${\ell }_{\infty }$ 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.

13 pages