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There is no bilinear Bishop-Phelps theorem

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Abstract

We answer a question posed by R. Aron, C. Finet and E. Werner, on the bilinear version of the Bishop-Phelps theorem, by exhibiting an example of a Banach spaceX such that the set of norm-attaining bilinear forms onX×X is not dense in the space of all continuous bilinear forms.

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Authors and Affiliations

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

    María D. Acosta, Francisco J. Aguirre & Rafael Payá

Authors
  1. María D. Acosta
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  2. Francisco J. Aguirre
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  3. Rafael Payá
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Corresponding author

Correspondence to María D. Acosta.

Additional information

Research partially supported by D.G.I.C.Y.T., project no. PB93-1142.

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Acosta, M.D., Aguirre, F.J. & Payá, R. There is no bilinear Bishop-Phelps theorem. Israel J. Math. 93, 221–227 (1996). https://doi.org/10.1007/BF02761104

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  • DOI: https://doi.org/10.1007/BF02761104

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