Basic topological and geometric properties of Cesáro-Orlicz spaces

Basic topological and geometric properties of Cesáro-Orlicz spaces

Necessary and sufficient conditions under which the Cesàro-Orlicz sequence space CESøis nontrivial are presented. It is proved that for the Luxemburg norm, Cesàro-Orlicz spaces cesøhave the Fatou property. Consequently, the spaces are complete. It is also proved that the subspace of order continuous...

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Main Authors: Yunan Cui, Henryk Hudzik, Narin Petrot, Suthep Suantai, Alicja Szymaszkiewicz
Format: Journal
Published: 2018
Subjects:
Mathematics
Online Access:https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=29044432840&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/62295
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Institution: Chiang Mai University
id th-cmuir.6653943832-62295
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spelling th-cmuir.6653943832-622952018-09-11T09:25:16Z Basic topological and geometric properties of Cesáro-Orlicz spaces Yunan Cui Henryk Hudzik Narin Petrot Suthep Suantai Alicja Szymaszkiewicz Mathematics Necessary and sufficient conditions under which the Cesàro-Orlicz sequence space CESøis nontrivial are presented. It is proved that for the Luxemburg norm, Cesàro-Orlicz spaces cesøhave the Fatou property. Consequently, the spaces are complete. It is also proved that the subspace of order continuous elements in cesøcan be defined in two ways. Finally, criteria for strict monotonicity, uniform monotonicity and rotundity (= strict convexity) of the spaces cesøare given. 2018-09-11T09:25:16Z 2018-09-11T09:25:16Z 2005-01-01 Journal 02534142 2-s2.0-29044432840 10.1007/BF02829808 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=29044432840&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/62295
institution Chiang Mai University
building Chiang Mai University Library
country Thailand
collection CMU Intellectual Repository
topic Mathematics
spellingShingle Mathematics
Yunan Cui
Henryk Hudzik
Narin Petrot
Suthep Suantai
Alicja Szymaszkiewicz
Basic topological and geometric properties of Cesáro-Orlicz spaces
description Necessary and sufficient conditions under which the Cesàro-Orlicz sequence space CESøis nontrivial are presented. It is proved that for the Luxemburg norm, Cesàro-Orlicz spaces cesøhave the Fatou property. Consequently, the spaces are complete. It is also proved that the subspace of order continuous elements in cesøcan be defined in two ways. Finally, criteria for strict monotonicity, uniform monotonicity and rotundity (= strict convexity) of the spaces cesøare given.
format Journal
author Yunan Cui
Henryk Hudzik
Narin Petrot
Suthep Suantai
Alicja Szymaszkiewicz
author_facet Yunan Cui
Henryk Hudzik
Narin Petrot
Suthep Suantai
Alicja Szymaszkiewicz
author_sort Yunan Cui
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 2018
url https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=29044432840&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/62295
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