On Chebyshev centers in Banach spaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912808934834176 |
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| author | Das, Syamantak Paul, Tanmoy |
| author_facet | Das, Syamantak Paul, Tanmoy |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_11087 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Chebyshev centers in Banach spaces Das, Syamantak Paul, Tanmoy Functional Analysis 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. |
| title | On Chebyshev centers in Banach spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2508.11087 |