On banach spaces with the approximate hyperplane series property

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

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We present a sufficient condition for a Banach space to have the approximate hyperplane series property (AHSP) which actually covers all known examples. We use this property to get a stability result to vector-valued spaces of integrable functions. On the other hand, the study of a possible Bishop-Phelps-Bollobás version of a classical result of V. Zizler leads to a new characterization of the AHSP for dual spaces in terms of w*-continuous operators and other related results.

Original languageEnglish
Pages (from-to)243-258
Number of pages16
JournalBanach Journal of Mathematical Analysis
Volume9
Issue number4
DOIs
StatePublished - 2015

Keywords

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

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