Basic topological and geometric properties of Cesáro-Orlicz spaces - Cui Y. (2014)
Necessary and sufficient conditions under which the Cesàro-Orlicz sequence space CESø is nontrivial are presented. It is proved that for the Luxemburg norm, Cesàro-Orlicz spaces cesø have the Fatou property. Consequently, the spaces are complete. It is also proved that the subspace of order continuous elements in cesø can be defined in two ways. Finally, criteria for strict monotonicity, uniform monotonicity and rotundity (= strict convexity) of the spaces ces ø are given.