The Bishop-Phelps-Bollobás theorem for operators on L1(μ)

Yun Sung Choi, Sun Kwang Kim, Han Ju Lee, Miguel Martín

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

In this paper we show that the Bishop-Phelps-Bollobás theorem holds for L(L1(μ),L1(ν)) for all measures μ and ν and also holds for L(L1(μ),L∞(ν)) for every arbitrary measure μ and every localizable measure ν. Finally, we show that the Bishop-Phelps-Bollobás theorem holds for two classes of bounded linear operators from a real L1(μ) into a real C(K) if μ is a finite measure and K is a compact Hausdorff space. In particular, one of the classes includes all Bochner representable operators and all weakly compact operators.

Original languageEnglish
Pages (from-to)214-242
Number of pages29
JournalJournal of Functional Analysis
Volume267
Issue number1
DOIs
StatePublished - 1 Jul 2014

Keywords

  • Approximation
  • Banach space
  • Bishop-Phelps-Bollobás theorem
  • Norm-attaining operators

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