Representation of Banach lattices as L1w spaces of a vector measure defined on a δ-ring

In this paper we prove that every Banach lattice having the Fatou property and having its s-order continuous part as an order dense subset, can be represented as the space L1 w(n) of weakly integrable functions with respect to some vector measure n defined on a d-ring.

Detalhes bibliográficos
Autores: Delgado Garrido, Olvido, Juan, M. A.
Formato: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2012
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/103718
Acesso em linha:https://hdl.handle.net/11441/103718
https://doi.org/10.36045/bbms/1337864270
Access Level:acceso abierto
Palavra-chave:Banach lattice
d-ring
Fatou property
Order density
Order continuity
Integration with respect to vector measures
Descrição
Resumo:In this paper we prove that every Banach lattice having the Fatou property and having its s-order continuous part as an order dense subset, can be represented as the space L1 w(n) of weakly integrable functions with respect to some vector measure n defined on a d-ring.