Linear extensions, almost isometries, and diameter two

• Trond A. Abrahamsen ^[1]
  1. [1] University of Agder

     University of Agder

     Noruega

     
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 30, Nº 2, 2015, págs. 135-151
• Idioma: inglés
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• Resumen

  • Heinrich, Mankiewicz, Sims, and Yost proved that every separable subspace of a Banach space Y is contained in a separable ideal in Y . We improve this result by replacing the term \ideal" with the term \almost isometric ideal". As a consequence of this we obtain, in terms of subspaces, characterizations of diameter 2 properties, the Daugavet property along with the properties of being an almost square space and an octahedral space.