Maurey-Rosenthal domination for abstract Banach lattices
We extend the Maurey-Rosenthal theorem on integral domination and factorization of p-concave operators from a p-convex Banach function space through Lp-spaces for the case of operators on abstract p-convex Banach lattices satisfying some essential lattice requirements - mainly order density of its o...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2013 |
| País: | España |
| Institución: | Universidad Católica de Valencia San Vicente Mártir |
| Repositorio: | RIUCV. Repositorio de la Universidad Católica de Valencia San Vicente Mártir |
| Idioma: | inglés |
| OAI Identifier: | oai:riucv.ucv.es:20.500.12466/5915 |
| Acceso en línea: | http://hdl.handle.net/20.500.12466/5915 |
| Access Level: | acceso abierto |
| Palabra clave: | Integral inequality Banach lattices p-convexity p-concavity 12 Matemáticas |
| Sumario: | We extend the Maurey-Rosenthal theorem on integral domination and factorization of p-concave operators from a p-convex Banach function space through Lp-spaces for the case of operators on abstract p-convex Banach lattices satisfying some essential lattice requirements - mainly order density of its order continuous part - that are shown to be necessary. We prove that these geometric properties can be characterized by means of an integral inequality giving a domination of the pointwise evaluation of the operator for a suitable weight also in the case of abstract Banach lattices. We obtain in this way what in a sense can be considered the most general factorization theorem of operators through Lp-spaces. In order to do this, we prove a new representation theorem for abstract p-convex Banach lattices with the Fatou property as spaces of p-integrable functions with respect to a vector measure. |
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