Basic Topological and Geometric Properties of Cesà ro–Orlicz Spaces

[摘要] Necessary and sufficient conditions under which the Cesàro–Orlicz sequence space $mathrm{ces}_𝜙$ is nontrivial are presented. It is proved that for the Luxemburg norm, Cesàro–Orlicz spaces $mathrm{ces}_𝜙$ have the Fatou property. Consequently, the spaces are complete. It is also proved that the subspace of order continuous elements in $mathrm{ces}_𝜙$ can be defined in two ways. Finally, criteria for strict monotonicity, uniform monotonicity and rotundity (= strict convexity) of the spaces $mathrm{ces}_𝜙$ are given.

[学科分类] 数学（综合）

[关键词] Cesàro–Orlicz sequence space;Luxemburg norm;Fatou property;order continuity;strict monotonicity;uniform monotonicity;rotundity.