Basic topological and geometric properties of Cesàro--Orlicz spaces

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dc.creatorCui, Yunan
dc.creatorHudzik, Henryk
dc.creatorPetrot, Narin
dc.creatorSuantai, Suthep
dc.creatorSzymaszkiewicz, Alicja
dc.date2006-07-28
dc.date.accessioned2026-07-07T07:21:05Z
dc.date.available2026-07-07T07:21:05Z
dc.descriptionNecessary and sufficient conditions under which the Cesàro--Orlicz sequence space $\cfi$ is nontrivial are presented. It is proved that for the Luxemburg norm, Cesàro--Orlicz spaces $\cfi$ have the Fatou property. Consequently, the spaces are complete. It is also proved that the subspace of order continuous elements in $\cfi$ can be defined in two ways. Finally, criteria for strict monotonicity, uniform monotonicity and rotundity (= strict convexity) of the spaces $\cfi$ are given.
dc.description16 pages
dc.identifierhttps://arxiv.org/abs/math/0607730
dc.identifierhttp://arxiv.org/abs/math/0607730
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115180
dc.subjectFunctional Analysis
dc.subject46B20, 46B45, 46E30
dc.titleBasic topological and geometric properties of Cesàro--Orlicz spaces
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