Local Bishop–Phelps–Bollobás properties

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

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11 Scopus citations

Abstract

In this paper we introduce some local versions of Bishop–Phelps–Bollobás type property for operators. That is, the function η which appears in their definitions depends not only on a given ε>0, but also on either a fixed norm-one operator T or a fixed norm-one vector x. We investigate those properties and show differences between local and uniform versions.

Original languageEnglish
Pages (from-to)304-323
Number of pages20
JournalJournal of Mathematical Analysis and Applications
Volume468
Issue number1
DOIs
StatePublished - 1 Dec 2018

Keywords

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

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