Strong subdifferentiability and local Bishop–Phelps–Bollobás properties

Sheldon Dantas, Sun Kwang Kim, Han Ju Lee, Martin Mazzitelli

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Abstract

Some local versions of the Bishop–Phelps–Bollobás property for operators have been recently presented in Dantas et al. (J Math Anal Appl 468(1):304–323, 2018). In the present article, we continue studying these properties for multilinear mappings. We show some differences between the local and uniform versions of these and also provide some interesting examples which show that this study is not just a mere generalization of the linear case. As a consequence of our results, we get that, for 2 < p, q< ∞, the norm of the projective tensor product ℓp⊗ ^ πq is strongly subdifferentiable. Moreover, we present necessary and sufficient conditions for the norm of a Banach space Y to be strongly subdifferentiable through the study of these properties for bilinear mappings on ℓ1N×Y.

Original languageEnglish
Article number47
JournalRevista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
Volume114
Issue number2
DOIs
StatePublished - 1 Apr 2020

Keywords

  • Banach space
  • Bishop–Phelps–Bollobás property
  • Norm attaining operators

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