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