Basic topological and geometric properties of Cesàro-Orlicz spaces |
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| Authors: | Yunan Cui Henryk Hudzik Narin Petrot Suthep Suantai Alicja Szymaszkiewicz |
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| Institution: | (1) Department of Mathematics, Harbin University of Science and Technology, 150 080 Harbin, People’s Republic of China;(2) Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland;(3) Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, Thailand;(4) Institut of Mathematics, Technical University, Szczecin, Poland |
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| 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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| Keywords: | Cesaro-Orlicz sequence space Luxemburg norm Fatou property order continuity strict monotonicity uniform monotonicity rotundity |
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