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arXiv · 2508.11087

On Chebyshev centers in Banach spaces

Syamantak Das·Tanmoy Paul
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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.

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Syamantak Das, Tanmoy Paul. 2025-08-14. On Chebyshev centers in Banach spaces. https://arxiv.org/abs/2508.11087

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