Polynomial numerical indices of Banach spaces with 1-unconditional bases

Han Ju Lee, Miguel Martín

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

The only infinite-dimensional complex space with 1-unconditional basis which has polynomial numerical index of order 2 equal to 1 is c 0. In the real case, there is no space of this type. We also show that, in the complex case, if X is an infinite-dimensional Banach sequence space with absolute norm whose Köthe dual is norming and has polynomial numerical index of order 2 equal to 1, then c 0⊂X⊂ℓ . In the real case, again there is no space of this type.

Original languageEnglish
Pages (from-to)2001-2008
Number of pages8
JournalLinear Algebra and Its Applications
Volume437
Issue number8
DOIs
StatePublished - 15 Oct 2012

Keywords

  • Absolute norm
  • Köthe space
  • Numerical index
  • Polynomial
  • Unconditional basis

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