Basic topological and geometric properties of Cesàro--Orlicz spaces

Details Basic topological and geometric properties of Cesàro--Orlicz spaces Basic topological and geometric properties of Cesàro--Orlicz spaces

2006-07-28

arxiv.org/abs/math/0607730v1

Mathematics

Functional Analysis

16 pages

Scientific paper

Necessary and sufficient conditions under which the Ces\`{a}ro--Orlicz sequence space $\cfi$ is nontrivial are presented. It is proved that for the Luxemburg norm, Ces\`{a}ro--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.

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