| Autor: |
Campo Acosta, Ricardo del, Fernández Carrión, Antonio, Mayoral Masa, Fernando, Naranjo Naranjo, Francisco José |
| Přispěvatelé: |
Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII), Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI), Universidad de Sevilla. FQM-133: Investigación en Análisis Funcional, Junta de Andalucía |
| Jazyk: |
angličtina |
| Rok vydání: |
2020 |
| Předmět: |
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| Popis: |
We characterize the relatively compact subsets of the order continuous part Ea of a quasi Banach function space E showing that the strong connection between compactness, uniform absolute continuity, uniform integrability, almost order boundedness and L-weak compact ness that appears in the classical setting of Lebesgue spaces remains almost invariant in this new context under mild assumptions. We also present a de la Vallée–Poussin type theorem in this context that allows us to locate each compact subset of Ea as a compact subset of a smaller quasi-Banach Orlicz space E Φ . Our results generalize the previous known results for the Banach function spaces L 1 (m) and L 1 w(m) associated to a vector measure m and moreover they can also be applied to the quasi-Banach function space L 1 ( m ) associated to the semivariation of m. Junta de Andalucía FQM-133 |
| Databáze: |
OpenAIRE |
| Externí odkaz: |
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