Polynomial numerical indices of Banach spaces with absolute norm

Han Ju Lee, Miguel Martín, Javier Merí

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

We study when a Banach space with absolute norm may have polynomial numerical indices equal to one. In the real case, we show that a Banach space X with absolute norm, which has the Radon-Nikodým property or is Asplund, satisfies n(2)(X)<1 unless it is one-dimensional. In the complex case, we show that the only Banach spaces X with absolute norm and the Radon-Nikodým property which satisfy n(2)(X)=1 are the spaces ℓ∞m. Also, the only Asplund complex space X with absolute norm which satisfies n(2)(X)=1 is c0(Λ).

Original languageEnglish
Pages (from-to)400-408
Number of pages9
JournalLinear Algebra and Its Applications
Volume435
Issue number2
DOIs
StatePublished - 15 Jul 2011

Keywords

  • Absolute norm
  • Köthe space
  • Numerical index
  • Polynomial

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