Regular methods of summability and the weak s-Fatou property in abstract Banach lattices of integrable functions
Consider an abstract Banach lattice. Under some mild assumptions, it can be identified with a Banach ideal of integrable functions with respect to a (non necessarily σ-finite) vector measure on a σ-ring. Extending some nowadays well-known results for the Komlós property involving Cesaro sums, we pro...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| 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:20.500.12466/5922 |
| Acceso en línea: | http://hdl.handle.net/20.500.12466/5922 |
| Access Level: | acceso abierto |
| Palabra clave: | Banach lattices Fatou property Integrable functions Regular methods of summability Vector measure 12 Matemáticas |
| Sumario: | Consider an abstract Banach lattice. Under some mild assumptions, it can be identified with a Banach ideal of integrable functions with respect to a (non necessarily σ-finite) vector measure on a σ-ring. Extending some nowadays well-known results for the Komlós property involving Cesaro sums, we prove that the weak s-Fatou property for a Banach lattice of integrable functions E is equivalent to the existence for each norm bounded sequence ( fn) in E of a regular method of summability D such that the sequence ( f D n) converges. |
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