### 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}e_{n}{double pipe} = 1 (n ∈ ℕ), where {e_{n}}_{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 = l_{p} (1 ≤ p < ∞) or E = c_{0}.

Original language | English (US) |
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Pages (from-to) | 212-215 |

Number of pages | 4 |

Journal | Functional Analysis and Its Applications |

Volume | 44 |

Issue number | 3 |

DOIs | |

State | Published - 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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## Cite this

*Functional Analysis and Its Applications*,

*44*(3), 212-215. https://doi.org/10.1007/s10688-010-0026-x