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Relatively weakly open sets in closed balls of Banach spaces, and the centralizer

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Abstract

We prove that, if the centralizer of a Banach space X is infinite-dimensional, then every nonempty relatively weakly open subset of the closed unit ball of X has diameter equal to 2. This result, together with a suitable refinement also proven in the paper, contains (and improves in some cases) previously known facts for C *-algebras, JB *-triples, spaces of vector valued continuous functions, and spaces of operators.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain

    Julio Becerra Guerrero

  2. Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain

    Angel Rodríguez-Palacios

Authors
  1. Julio Becerra Guerrero
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  2. Angel Rodríguez-Palacios
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Correspondence to Angel Rodríguez-Palacios.

Additional information

Partially supported by Junta de Andalucía grants FQM 0199 and FQM 1215, and Project I+D MCYT MTM-2004-03882 and MTM-2006-15546-C02-02.

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Becerra Guerrero, J., Rodríguez-Palacios, A. Relatively weakly open sets in closed balls of Banach spaces, and the centralizer. Math. Z. 262, 557–570 (2009). https://doi.org/10.1007/s00209-008-0389-3

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