A Banach Lattice Having the Approximation Property, but not Having the Bounded Approximation Property

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Abstract

Abstract: The first example of a Banach space with the approximation property but without the bounded approximation property was given by Figiel and Johnson in 1973. We give the first example of a Banach lattice with the approximation property but without the bounded approximation property. As a consequence, we prove the existence of an integral operator (in the sense of Grothendieck) on a Banach lattice which is not strictly integral.

Original languageEnglish
Pages (from-to)243-249
Number of pages7
JournalMathematical Notes
Volume108
Issue number1-2
DOIs
StatePublished - 1 Jul 2020

Scopus subject areas

  • Mathematics(all)

Keywords

  • approximation property
  • Banach lattice
  • basis
  • bounded approximation property

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