Uniformly Nonsquare in Orlicz Space Equipped with the Mazur-Orlicz F-Norm
The definition of uniformly nonsquareness in Banach spaces is extended to F-normed spaces. Most of the results from this paper concern (uniformly) nonsquareness in the sense of James or in the sense of Schäffer in Orlicz spaces equipped with the Mazur-Orlicz F-norm. It is well known that uniform non...
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| Format: | Article |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/6618846 |
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| author | Yunan Cui Tongyu Wang |
| author_facet | Yunan Cui Tongyu Wang |
| author_sort | Yunan Cui |
| collection | DOAJ |
| description | The definition of uniformly nonsquareness in Banach spaces is extended to F-normed spaces. Most of the results from this paper concern (uniformly) nonsquareness in the sense of James or in the sense of Schäffer in Orlicz spaces equipped with the Mazur-Orlicz F-norm. It is well known that uniform nonsquareness in the sense of Schäffer and in the sense of James are equivalent in Banach spaces. In this paper, we found that uniform nonsquareness in the sense of James and in the sense of Schäffer are not equivalent for F-normed spaces. Criteria for Orlicz spaces equipped with the Mazur-Orlicz F-norm to be nonsquare and uniformly nonsquare in the sense of James or in the sense of Schäffer are given. |
| format | Article |
| id | doaj-art-86943b505089498b871fcf944d1c7fdf |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-86943b505089498b871fcf944d1c7fdf2025-02-03T01:20:44ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/66188466618846Uniformly Nonsquare in Orlicz Space Equipped with the Mazur-Orlicz F-NormYunan Cui0Tongyu Wang1Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, ChinaDepartment of Mathematics, Harbin University of Science and Technology, Harbin 150080, ChinaThe definition of uniformly nonsquareness in Banach spaces is extended to F-normed spaces. Most of the results from this paper concern (uniformly) nonsquareness in the sense of James or in the sense of Schäffer in Orlicz spaces equipped with the Mazur-Orlicz F-norm. It is well known that uniform nonsquareness in the sense of Schäffer and in the sense of James are equivalent in Banach spaces. In this paper, we found that uniform nonsquareness in the sense of James and in the sense of Schäffer are not equivalent for F-normed spaces. Criteria for Orlicz spaces equipped with the Mazur-Orlicz F-norm to be nonsquare and uniformly nonsquare in the sense of James or in the sense of Schäffer are given.http://dx.doi.org/10.1155/2021/6618846 |
| spellingShingle | Yunan Cui Tongyu Wang Uniformly Nonsquare in Orlicz Space Equipped with the Mazur-Orlicz F-Norm Journal of Function Spaces |
| title | Uniformly Nonsquare in Orlicz Space Equipped with the Mazur-Orlicz F-Norm |
| title_full | Uniformly Nonsquare in Orlicz Space Equipped with the Mazur-Orlicz F-Norm |
| title_fullStr | Uniformly Nonsquare in Orlicz Space Equipped with the Mazur-Orlicz F-Norm |
| title_full_unstemmed | Uniformly Nonsquare in Orlicz Space Equipped with the Mazur-Orlicz F-Norm |
| title_short | Uniformly Nonsquare in Orlicz Space Equipped with the Mazur-Orlicz F-Norm |
| title_sort | uniformly nonsquare in orlicz space equipped with the mazur orlicz f norm |
| url | http://dx.doi.org/10.1155/2021/6618846 |
| work_keys_str_mv | AT yunancui uniformlynonsquareinorliczspaceequippedwiththemazurorliczfnorm AT tongyuwang uniformlynonsquareinorliczspaceequippedwiththemazurorliczfnorm |