The Bishop-Phelps-Bollobás property for operators from L∞(μ) to uniformly convex Banach spaces

Sun Kwang Kim, Han Ju Lee, Pei Kee Lin

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Let X = L∞(μ) and Y be uniformly convex Banach space. We show that the pair (X, Y) has the Bishop-Phelps-Bollobás property for any measure space (Ω, μ). This solves a question raised by Acosta, Aron, Garcia, and Maestre. We also prove that if X is either complex L∞(μ) or complex c0, and Y is complex uniformly convex, then the pair (X, Y) also has the Bishop-Phelps-Bollobás property.

Original languageEnglish
Pages (from-to)243-249
Number of pages7
JournalJournal of Nonlinear and Convex Analysis
Volume17
Issue number2
StatePublished - Feb 2016

Keywords

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

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