Regular methods of summability and the weak sigma-Fatou property in abstract Banach lattices of integrable functions
[EN] Consider an abstract Banach lattice. Under some mild assumptions, it can be identi¿ed with a Banach ideal of integrable functions with respect to a (non necessarily ¿-¿nite) vector measure on a ¿-ring. Extending some nowadays well-known results for the Koml¿os property involving Cesaro sums, we...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/122501 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/122501 |
| Access Level: | acceso abierto |
| Palabra clave: | Banach lattice Fatou property Regular methods Summability Integrable functions Vector measure MATEMATICA APLICADA |
| Sumario: | [EN] Consider an abstract Banach lattice. Under some mild assumptions, it can be identi¿ed with a Banach ideal of integrable functions with respect to a (non necessarily ¿-¿nite) vector measure on a ¿-ring. Extending some nowadays well-known results for the Koml¿os property involving Cesaro sums, we prove that the weak ¿-Fatou property is equivalent to the existence of a regular method of summability D of any norm bounded sequence in the space. |
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