Thickness of the unit sphere, l1-types, and the almost Daugavet property

• Autores: Vladimir Kadets, Varvara Shepelska, Dirk Werner
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 37, Nº 3, 2011, págs. 867-878
• Idioma: inglés
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• Resumen

  • We study those Banach spaces X for which SX does not admit a finite ?-net consisting of elements of SX for any ? < 2. We give characterisations of this class of spaces in terms of l1-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 l1.