Interpolation of operators when the extreme spaces are L^∞

1991/04/29 by Jesús Bastero, Bastero, Jesús, Francisco J. Ruiz +1
Mathematics · #46E #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.FA #msc:46E

paper · pdf · doi:10.48550/arxiv.math/9201226

arxiv created 1991/04/29 · openalex publication_date 1991/04/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, equivalence between interpolation properties of linear operators and monotonicity conditions are studied, for a pair (X₀,X₁) of rearrangement invariant quasi Banach spaces, when the extreme spaces of the interpolation are L^∞ and a pair (A₀,A₁) under some assumptions. Weak and restricted weak intermediate spaces fall in our context. Applications to classical Lorentz and Lorentz-Orlicz spaces are given.

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