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A characterization of reflexive spaces

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Abstract

We prove that a Banach space is reflexive if for every equivalent norm, the set of norm attaining functionals has non-empty norm-interior in the dual space. It is also proved that the set of norm attaining functionals on a Banach space that is not a Grothendieck space is not a w*-G δ subset of the dual space.

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Authors and Affiliations

  1. Departamento de Análisis Matemático, Universidad de Granada, 18071, Granada, Spain

    María D. Acosta

  2. Department of Mechanics and Mathematics, Kharkov National University, pl. Svobody 4, Kharkov, 61077, Ukraine

    Vladimir Kadets

Authors
  1. María D. Acosta
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  2. Vladimir Kadets
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Corresponding author

Correspondence to María D. Acosta.

Additional information

The first author was supported by MEC Project MTM-2009-07498 and Junta de Andalucía grant FQM-4011. The second author was supported by Junta de Andalucía and FEDER grant P06-FQM-01438.

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Acosta, M.D., Kadets, V. A characterization of reflexive spaces. Math. Ann. 349, 577–588 (2011). https://doi.org/10.1007/s00208-010-0528-0

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  • DOI: https://doi.org/10.1007/s00208-010-0528-0

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