Preprint No. A-08-08

Vladimir Kadets, Varvara Shepelska, Dirk Werner

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

Abstract: 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 $\ell_1$.

Keywords: Daugavet property, $\ell_1$-subspace, types, thickness

Mathematics Subject Classification (MSC2000): 46B04; 46B03, 46B25

Language: ENG


Contact: Dirk Werner, Freie Universität Berlin, Fachbereich Mathematik und Informatik,
Arnimallee 6, D-14195 Berlin, Germany (

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