The Bishop-Phelps-Bollobás property for bilinear forms and polynomials

María D. Acosta, Julio Becerra-Guerrero, Yun Sung Choi, Domingo Garcia, Sun Kwang Kim, Han Ju Lee, Manuel Maestre

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6 Scopus citations

Abstract

For a ς-finite measure μ and a Banach space Y we study the Bishop-Phelps-Bollobás property (BPBP) for bilinear forms on L1(μ)×Y , that is, a (continuous) bilinear form on L1(μ)×Y almost attaining its norm at (f0; y0) can be approximated by bilinear forms attaining their norms at unit vectors close to (f0; y0). In case that Y is an Asplund space we characterize the Banach spaces Y satisfying this property. We also exhibit some class of bilinear forms for which the BPBP does not hold, though the set of norm attaining bilinear forms in that class is dense.

Original languageEnglish
Pages (from-to)957-979
Number of pages23
JournalJournal of the Mathematical Society of Japan
Volume66
Issue number3
DOIs
StatePublished - 2014

Keywords

  • Banach space
  • Bilinear form
  • Bishop-Phelps-Bollobás Theorem
  • Norm attaining
  • Polynomial

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