Analytic and Ck approximations of norms in separable Banach spaces

Robert Deville, Vladimir Fonf, Petr Hájek

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

We prove that in separable Hilbert spaces, in ℓp(Nℕ) for p an even integer, and in Lp[0,1] for p an even integer, every equivalent norm can be approximated uniformly on bounded sets by analytic norms. In ℓp(Nℕ) and in Lp[0,1] for p ∉ Nℕ (resp. for p an odd integer), every equivalent norm can be approximated uniformly on bounded sets by C[p]-smooth norms (resp. by Cp-1-smooth norms).

Original languageEnglish
Pages (from-to)61-74
Number of pages14
JournalStudia Mathematica
Volume120
Issue number1
StatePublished - 1 Dec 1996

Keywords

  • Analytic norm
  • Approximation
  • Convex function
  • Geometry of Banach spaces

ASJC Scopus subject areas

  • General Mathematics

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