On stability of κ-monotonicity of Banach couples

Sergey V. Astashkin, Konstantin E. Tikhomirov

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2 Scopus citations

Abstract

Suppose that E is a separable Banach lattice of two-sided real sequences such that en = 1 (n ε ℕ), where {en}nε ℤ is the standard basis. One of the main aims of this paper is a characterization of couples E→ = (E, E(2)) whose κ-monotonicity is stable when multiplying the weight by a constant. It is shown that such a property holds only for a couple E→ constructed upon a shift-invariant lattice. We construct also a non-trivial example of shift-invariant separable Banach lattice E such that the couple E→ is κ-monotone. The last result contrasts with the following well-known theorem due to Kalton: if E is a separable symmetric Banach lattice such that the couple E→ is κ-monotone then either E = lp (1 ≤ p< ∞) or E = c0..

Original languageEnglish (US)
Pages (from-to)113-137
Number of pages25
JournalRevista Matematica Complutense
Volume23
Issue number1
DOIs
StatePublished - Jan 2010

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Banach lattices
  • Calderó
  • Interpolation of operators
  • Monotone Banach couples
  • N-Lozanovskiǐ
  • Peetre -functional
  • Real method of interpolation
  • Shift-invariant spaces
  • Spaces
  • κ

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