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...

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Detalles Bibliográficos
Autores: Jiménez Fernández, Eduardo, Juan Blanco, María Aranzazu, Sánchez Pérez, Enrique Alfonso|||0000-0001-8854-3154
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
Descripción
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.