A note on symmetric separation in Banach spaces

Tommaso Russo

doi:10.1007/s13398-019-00722-4

paper

A note on symmetric separation in Banach spaces

arXiv:1904.12598 · doi:10.1007/s13398-019-00722-4

Abstract

We present some new results on the symmetric Kottman's constant $K^{s} (X)$ of a Banach space $X$ and its relationship with the Kottman constant. We show that $K^{s} (X) > 1$ , for every infinite-dimensional Banach space, thereby solving a problem by J.M.F. Castillo and P.L. Papini. We also investigate such constant in the class of Banach spaces admitting $c_{0}$ spreading models, answering in particular one question from our previous joint paper with P. Hájek and T. Kania.

10 pp