A Banach space in which all compact sets, but not all bounded sets, admit Chebyshev centers |
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Authors: | Libor Veselý |
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Institution: | (1) Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Via C. Saldini 50, 20133 Milano, Italy |
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Abstract: | Given a Banach spaceX, letc
0(X) be the space of all null sequences inX (equipped with the supremum norm). We show that: 1) each compact set inc
0(X) admits a (Chebyshev) center iff each compact set inX admits a center; 2) forX satisfying a certain condition (Q), each bounded set inc
0(X) admits a center iffX is quasi uniformly rotund. We construct a Banach spaceX such that the compact subsets ofX admit centers,X satisfies the condition (Q) andX is not quasi uniformly rotund. It follows that the Banach spaceE=c
0(X) has the property from the title.
Eine überarbeitete Fassung ging am 4. 7. 2001 ein |
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Keywords: | Primary 41A65 Secondary 46B45 |
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