## Abstract

Suppose that E is a separable Banach lattice of two-sided real sequences such that e_{n} = 1 (n ε ℕ), where {e_{n}}nε ℤ is the standard basis. One of the main aims of this paper is a characterization of couples E→ = (E, E(2^{-κ})) 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 = l_{p} (1 ≤ p< ∞) or E = c_{0.}.

Original language | English (US) |
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Pages (from-to) | 113-137 |

Number of pages | 25 |

Journal | Revista Matematica Complutense |

Volume | 23 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2010 |

## All Science Journal Classification (ASJC) codes

- General Mathematics

## Keywords

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