Representation and factorization theorems for almost-L-p-spaces
[EN] We extend the notions of p-convexity and p-concavity for Banach ideals of measurable functions following an asymptotic procedure. We prove a representation theorem for the spaces satisfying both properties as the one that works for the classical case: each almost p-convex and almost p-concave s...
| Autores: | , , , |
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| Formato: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Recursos: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/155063 |
| Acesso em linha: | https://riunet.upv.es/handle/10251/155063 |
| Access Level: | acceso abierto |
| Palavra-chave: | Banach lattice P-convexity P-concavity, L-p-space MATEMATICA APLICADA |
| Resumo: | [EN] We extend the notions of p-convexity and p-concavity for Banach ideals of measurable functions following an asymptotic procedure. We prove a representation theorem for the spaces satisfying both properties as the one that works for the classical case: each almost p-convex and almost p-concave space is order isomorphic to an almost-L-p-space. The class of almost-L-p-spaces contains, in particular, direct sums of (infinitely many) L-p-spaces with different norms, that are not in general p-convex nor p-concave -. We also analyze in this context the extension of the Maurey Rosenthal factorization theorem that works for p-concave operators acting in p-convex spaces. In this way we provide factorization results that allow to deal with more general factorization spaces than L-p-spaces. (C) 2019 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved. |
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