Artículo
Compactness in quasi-Banach function spaces with applications to L1 of the semivariation of a vector measure
Autor/es | Campo Acosta, Ricardo del
Fernández Carrión, Antonio Mayoral Masa, Fernando Naranjo Naranjo, Francisco José |
Departamento | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI) |
Fecha de publicación | 2020 |
Fecha de depósito | 2022-07-28 |
Publicado en |
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Resumen | 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, ... 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. |
Agencias financiadoras | Junta de Andalucía |
Identificador del proyecto | FQM-133 |
Cita | Campo Acosta, R.d., Fernández Carrión, A., Mayoral Masa, F. y Naranjo Naranjo, F.J. (2020). Compactness in quasi-Banach function spaces with applications to L1 of the semivariation of a vector measure. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 114 (3, art. nº112) |
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