On stably K-monotone Banach couples

S. V. Astashkin, K. E. Tikhomirov

Research output: Contribution to journalArticle

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Abstract

The K-monotonicity of Banach couples which is stable with respect to multiplication of weight by a constant is studied. Suppose that E is a separable Banach lattice of two-sided sequences of reals such that {double pipe}en{double pipe} = 1 (n ∈ ℕ), where {en}n∈ℤ is the canonical basis. It is shown that, is a stably K-monotone couple if and only if, is K-monotone and E is shift-invariant. A non-trivial example of a shift-invariant separable Banach lattice E such that the couple, is K-monotone is constructed. This result contrasts with the following well-known theorem of Kalton: If E is a separable symmetric sequence space such that the couple, is K-monotone, then either E = lp (1 ≤ p < ∞) or E = c0.

Original languageEnglish (US)
Pages (from-to)212-215
Number of pages4
JournalFunctional Analysis and Its Applications
Volume44
Issue number3
DOIs
StatePublished - Sep 30 2010

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Keywords

  • K-monotone Banach couple
  • Peetre K-functional
  • interpolation of operators
  • shift-invariant space

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