Basic topological and geometric properties of Cesáro-Orlicz spaces

Abstract

Necessary and sufficient conditions under which the Cesàro-Orlicz sequence space CESøis nontrivial are presented. It is proved that for the Luxemburg norm, Cesàro-Orlicz spaces cesøhave the Fatou property. Consequently, the spaces are complete. It is also proved that the subspace of order continuous elements in cesøcan be defined in two ways. Finally, criteria for strict monotonicity, uniform monotonicity and rotundity (= strict convexity) of the spaces cesøare given.