Abstract
Necessary and sufficient conditions under which the Cesàro-Orlicz sequence spaceces ϕ is nontrivial are presented. It is proved that for the Luxemburg norm, Cesàro-Orlicz spacesces ϕ have the Fatou property. Consequently, the spaces are complete. It is also proved that the subspace of order continuous elements inces ϕ can be defined in two ways. Finally, criteria for strict monotonicity, uniform monotonicity and rotundity (= strict convexity) of the spacesces ϕ are given.
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Cui, Y., Hudzik, H., Petrot, N. et al. Basic topological and geometric properties of Cesàro-Orlicz spaces. Proc. Indian Acad. Sci. (Math. Sci.) 115, 461–476 (2005). https://doi.org/10.1007/BF02829808
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DOI: https://doi.org/10.1007/BF02829808