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Basic topological and geometric properties of Cesàro--Orlicz spaces

Yunan Cui·Henryk Hudzik·Narin Petrot·Suthep Suantai·Alicja Szymaszkiewicz
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Abstract

Necessary and sufficient conditions under which the Cesàro--Orlicz sequence space $\cfi$ is nontrivial are presented. It is proved that for the Luxemburg norm, Cesàro--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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Yunan Cui, Henryk Hudzik, Narin Petrot, Suthep Suantai, Alicja Szymaszkiewicz. 2006-07-28. Basic topological and geometric properties of Cesàro--Orlicz spaces. https://arxiv.org/abs/math/0607730

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