Repositorio de producción científica de la Universidad de Sevilla

Complete characterizations of Kadec-Klee properties in Orlicz spaces

Opened Access Complete characterizations of Kadec-Klee properties in Orlicz spaces
Estadísticas
Icon
Exportar a
Autor: Domínguez Benavides, Tomás
Hudzik, Henryk
López Acedo, Genaro
Mastylo, Mieczyslaw
Sims, Brailey
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2003
Publicado en: Houston Journal of Mathematics, 29 (4), 1027-1044.
Tipo de documento: Artículo
Resumen: We study the connections between the Kadec-Klee property for local convergence in measure H`, the Kadec-Klee property for global onvergence in measure Hg and the ∆2-condition for Orlicz function spaces Lϕ equipped with either the Luxemburg norm k · kϕ or the Orlicz norm k · k0 ϕ. Nominally, we prove that for (Lϕ, k · kϕ) the conditions: ϕ satisfies an appropriate ∆2-condition and Lϕ ∈ H`, Lϕ ∈ Hg are equivalent, although Lϕ ∈ Hg is not equivalent to Eϕ ∈ Hg. In contrast, we also prove that, in the case of a non-atomic infinite measure space, properties H` and Hg for (Lϕ, k · k0 ϕ) do not coincide. More precisely, we prove that if ϕ vanishes only at zero, then both these properties coincide and they are equivalent to ϕ ∈ ∆2. However, if ϕ vanishes outside zero, then (Lϕ, k · k0 ϕ) ∈ Hg if and only if ϕ ∈ ∆2(∞). Since in the last case (Lϕ, k k0 ϕ) is not order continuous, properties H` and Hg differ. Analogous results are also proved for the subspace Eϕ of Lϕ. It is also worth mentioni...
[Ver más]
Cita: Domínguez Benavides, T., Hudzik, H., López Acedo, G., Mastylo, M. y Sims, B. (2003). Complete characterizations of Kadec-Klee properties in Orlicz spaces. Houston Journal of Mathematics, 29 (4), 1027-1044.
Tamaño: 274.1Kb
Formato: PDF

URI: http://hdl.handle.net/11441/41800

Mostrar el registro completo del ítem


Esta obra está bajo una Licencia Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 Internacional

Este registro aparece en las siguientes colecciones