The Bishop-Phelps-Bollobás property for operators between spaces of continuous functions

María D. Acosta, Julio Becerra-Guerrero, Yun Sung Choi, Maciej Ciesielski, Sun Kwang Kim, Han Ju Lee, Mary Lilian Lourenço, Miguel Martín

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

We show that the space of bounded linear operators between spaces of continuous functions on compact Hausdorff topological spaces has the Bishop-Phelps-Bollobás property. A similar result is also proved for the class of compact operators from the space of continuous functions vanishing at infinity on a locally compact and Hausdorff topological space into a uniformly convex space, and for the class of compact operators from a Banach space into a predual of an L1-space.

Original languageEnglish
Pages (from-to)323-332
Number of pages10
JournalNonlinear Analysis, Theory, Methods and Applications
Volume95
DOIs
StatePublished - 2014

Keywords

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

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