Thickness of the unit sphere, $\ell_1$-types, and the almost Daugavet property

Details Thickness of the unit sphere, $\ell_1$-types, and the almost Daugavet property Thickness of the unit sphere, $\ell_1$-types, and the almost Daugavet property

2009-02-26

arxiv.org/abs/0902.4503v1

Mathematics

Functional Analysis

To appear in Houston Journal of Mathematics

Scientific paper

We study those Banach spaces $X$ for which $S_X$ does not admit a finite $\eps$-net consisting of elements of $S_X$ for any $\eps < 2$. We give characterisations of this class of spaces in terms of $\ell_1$-type sequences and in terms of the almost Daugavet property. The main result of the paper is: a separable Banach space $X$ is isomorphic to a space from this class if and only if $X$ contains an isomorphic copy of $\ell_1$.

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