On Chebyshev centers in Banach spaces

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 Veselý, 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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ArXiv.org
Published
2025-08-14
Primary Topic
Geochemistry and Geologic Mapping
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article
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article

On Chebyshev centers in Banach spaces

ArXiv.org
Geochemistry and Geologic Mapping
article

On Chebyshev centers in Banach spaces

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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 Veselý, 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.

ArXiv.org
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Geochemistry and Geologic Mapping
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On Chebyshev centers in Banach spaces · ArXiv.org (2025) | TGRS Research Map | TGRS