On Chebyshev centers in Banach spaces

Syamantak Das; Tanmoy Paul

On Chebyshev centers in Banach spaces

Functional Analysis 2026-01-09 v2

Authors: Syamantak Das , Tanmoy Paul

Abstract

In this note, we observe that $X\in (GC)$ if $X$ admits Chebyshev center for any finite set in it. This answers the problem raised by Vesel\'y, addressed in [{\em Generalized centers of finite sets in Banach spaces}, Acta Math. Univ. Comenian. (N.S.) {\bf 66}(1) (1997), 83--115]. We extend our observation towards the fact that the property $(GC)$ is not a 3-space property.

Cite

@article{arxiv.2508.11087,
  title  = {On Chebyshev centers in Banach spaces},
  author = {Syamantak Das and Tanmoy Paul},
  journal= {arXiv preprint arXiv:2508.11087},
  year   = {2026}
}

Comments

Some modifications on the results in this paper has been done. We are rewritting this work with a third collaborator

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