Small Pre-Quasi Banach Operator Ideals of Type Orlicz-Cesáro Mean Sequence Spaces
In this paper, we give the sufficient conditions on Orlicz-Cesáro mean sequence spaces cesφ, where φ is an Orlicz function such that the class Scesφ of all bounded linear operators between arbitrary Banach spaces with its sequence of s-numbers which belong to cesφ forms an operator ideal. The comple...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2019/7265010 |
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| author | Awad A. Bakery Mustafa M. Mohammed |
| author_facet | Awad A. Bakery Mustafa M. Mohammed |
| author_sort | Awad A. Bakery |
| collection | DOAJ |
| description | In this paper, we give the sufficient conditions on Orlicz-Cesáro mean sequence spaces cesφ, where φ is an Orlicz function such that the class Scesφ of all bounded linear operators between arbitrary Banach spaces with its sequence of s-numbers which belong to cesφ forms an operator ideal. The completeness and denseness of its ideal components are specified and Scesφ constructs a pre-quasi Banach operator ideal. Some inclusion relations between the pre-quasi operator ideals and the inclusion relations for their duals are explained. Moreover, we have presented the sufficient conditions on cesφ such that the pre-quasi Banach operator ideal generated by approximation number is small. The above results coincide with that known for cesp (1<p<∞). |
| format | Article |
| id | doaj-art-98390e2a029740c0ac26bad5cefbc59a |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-98390e2a029740c0ac26bad5cefbc59a2025-02-03T01:20:27ZengWileyJournal of Function Spaces2314-88962314-88882019-01-01201910.1155/2019/72650107265010Small Pre-Quasi Banach Operator Ideals of Type Orlicz-Cesáro Mean Sequence SpacesAwad A. Bakery0Mustafa M. Mohammed1Department of Mathematics, Faculty of Science and Arts, University of Jeddah(UJ), P.O. Box 355, Code 21921 Khulais, Saudi ArabiaDepartment of Mathematics, Faculty of Science and Arts, University of Jeddah(UJ), P.O. Box 355, Code 21921 Khulais, Saudi ArabiaIn this paper, we give the sufficient conditions on Orlicz-Cesáro mean sequence spaces cesφ, where φ is an Orlicz function such that the class Scesφ of all bounded linear operators between arbitrary Banach spaces with its sequence of s-numbers which belong to cesφ forms an operator ideal. The completeness and denseness of its ideal components are specified and Scesφ constructs a pre-quasi Banach operator ideal. Some inclusion relations between the pre-quasi operator ideals and the inclusion relations for their duals are explained. Moreover, we have presented the sufficient conditions on cesφ such that the pre-quasi Banach operator ideal generated by approximation number is small. The above results coincide with that known for cesp (1<p<∞).http://dx.doi.org/10.1155/2019/7265010 |
| spellingShingle | Awad A. Bakery Mustafa M. Mohammed Small Pre-Quasi Banach Operator Ideals of Type Orlicz-Cesáro Mean Sequence Spaces Journal of Function Spaces |
| title | Small Pre-Quasi Banach Operator Ideals of Type Orlicz-Cesáro Mean Sequence Spaces |
| title_full | Small Pre-Quasi Banach Operator Ideals of Type Orlicz-Cesáro Mean Sequence Spaces |
| title_fullStr | Small Pre-Quasi Banach Operator Ideals of Type Orlicz-Cesáro Mean Sequence Spaces |
| title_full_unstemmed | Small Pre-Quasi Banach Operator Ideals of Type Orlicz-Cesáro Mean Sequence Spaces |
| title_short | Small Pre-Quasi Banach Operator Ideals of Type Orlicz-Cesáro Mean Sequence Spaces |
| title_sort | small pre quasi banach operator ideals of type orlicz cesaro mean sequence spaces |
| url | http://dx.doi.org/10.1155/2019/7265010 |
| work_keys_str_mv | AT awadabakery smallprequasibanachoperatoridealsoftypeorliczcesaromeansequencespaces AT mustafammohammed smallprequasibanachoperatoridealsoftypeorliczcesaromeansequencespaces |