Download PDF by Vesely L.: A Banach space in which all compact sets, but not all

By Vesely L.

Given a Banach spaceX, letc 0(X) be the gap of all null sequences inX (equipped with the supremum norm). We convey that: 1) every one compact set inc 0(X) admits a (Chebyshev) heart iff every one compact set inX admits a middle; 2) forX pleasurable a definite situation (Q), every one bounded set inc 0(X) admits a middle iffX is quasi uniformly rotund. We build a Banach spaceX such that the compact subsets ofX admit centers,X satisfies the situation (Q) andX isn't quasi uniformly rotund. It follows that the Banach spaceE=c 0(X) has the valuables from the name.

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A Banach space in which all compact sets, but not all bounded sets, admit Chebyshev centers by Vesely L.


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