Basic topological and geometric properties of Cesáro-Orlicz spaces
Necessary and sufficient conditions under which the Cesàro-Orlicz sequence space CESø is nontrivial are presented. It is proved that for the Luxemburg norm, Cesàro-Orlicz spaces cesø have the Fatou property. Consequently, the spaces are complete. It is also proved that the subspace of order continuo...
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2014
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th-cmuir.6653943832-49352014-08-30T02:55:58Z Basic topological and geometric properties of Cesáro-Orlicz spaces Cui Y. Hudzik H. Petrot N. Suantai S. Szymaszkiewicz A. Necessary and sufficient conditions under which the Cesàro-Orlicz sequence space CESø is nontrivial are presented. It is proved that for the Luxemburg norm, Cesàro-Orlicz spaces cesø have the Fatou property. Consequently, the spaces are complete. It is also proved that the subspace of order continuous elements in cesø can be defined in two ways. Finally, criteria for strict monotonicity, uniform monotonicity and rotundity (= strict convexity) of the spaces ces ø are given. 2014-08-30T02:55:58Z 2014-08-30T02:55:58Z 2005 Conference Paper 02534142 PIAMD http://www.scopus.com/inward/record.url?eid=2-s2.0-29044432840&partnerID=40&md5=a34936a06e5f7549f37252a6866f3e26 http://cmuir.cmu.ac.th/handle/6653943832/4935 English |
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Necessary and sufficient conditions under which the Cesàro-Orlicz sequence space CESø is nontrivial are presented. It is proved that for the Luxemburg norm, Cesàro-Orlicz spaces cesø have the Fatou property. Consequently, the spaces are complete. It is also proved that the subspace of order continuous elements in cesø can be defined in two ways. Finally, criteria for strict monotonicity, uniform monotonicity and rotundity (= strict convexity) of the spaces ces ø are given. |
| format |
Conference or Workshop Item |
| author |
Cui Y. Hudzik H. Petrot N. Suantai S. Szymaszkiewicz A. |
| spellingShingle |
Cui Y. Hudzik H. Petrot N. Suantai S. Szymaszkiewicz A. Basic topological and geometric properties of Cesáro-Orlicz spaces |
| author_facet |
Cui Y. Hudzik H. Petrot N. Suantai S. Szymaszkiewicz A. |
| author_sort |
Cui Y. |
| title |
Basic topological and geometric properties of Cesáro-Orlicz spaces |
| title_short |
Basic topological and geometric properties of Cesáro-Orlicz spaces |
| title_full |
Basic topological and geometric properties of Cesáro-Orlicz spaces |
| title_fullStr |
Basic topological and geometric properties of Cesáro-Orlicz spaces |
| title_full_unstemmed |
Basic topological and geometric properties of Cesáro-Orlicz spaces |
| title_sort |
basic topological and geometric properties of cesáro-orlicz spaces |
| publishDate |
2014 |
| url |
http://www.scopus.com/inward/record.url?eid=2-s2.0-29044432840&partnerID=40&md5=a34936a06e5f7549f37252a6866f3e26 http://cmuir.cmu.ac.th/handle/6653943832/4935 |
| _version_ |
1681420330622517248 |