Pre-Quasi Simple Banach Operator Ideal Generated by s−Numbers
Let E be a weighted Nakano sequence space or generalized Cesáro sequence space defined by weighted mean and by using s−numbers of operators from a Banach space X into a Banach space Y. We give the sufficient (not necessary) conditions on E such that the components SEX,Y≔T∈LX,Y:snTn=0∞∈E of the class...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2020/9164781 |
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| author | Awad A. Bakery Afaf R. Abou Elmatty |
| author_facet | Awad A. Bakery Afaf R. Abou Elmatty |
| author_sort | Awad A. Bakery |
| collection | DOAJ |
| description | Let E be a weighted Nakano sequence space or generalized Cesáro sequence space defined by weighted mean and by using s−numbers of operators from a Banach space X into a Banach space Y. We give the sufficient (not necessary) conditions on E such that the components SEX,Y≔T∈LX,Y:snTn=0∞∈E of the class SE form pre-quasi operator ideal, the class of all finite rank operators are dense in the Banach pre-quasi ideal SE, the pre-quasi operator ideal formed by the sequence of approximation numbers is strictly contained for different weights and powers, the pre-quasi Banach Operator ideal formed by the sequence of approximation numbers is small, and finally, the pre-quasi Banach operator ideal constructed by s−numbers is simple Banach space. |
| format | Article |
| id | doaj-art-908dd0d459c842ac92c75e27509b86ef |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-908dd0d459c842ac92c75e27509b86ef2025-02-03T05:51:14ZengWileyJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/91647819164781Pre-Quasi Simple Banach Operator Ideal Generated by s−NumbersAwad A. Bakery0Afaf R. Abou Elmatty1University of Jeddah, College of Science and Arts at Khulis, Department of Mathematics, Jeddah, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Ain Shams University, P.O. Box 1156, Abbassia, Cairo 11566, EgyptLet E be a weighted Nakano sequence space or generalized Cesáro sequence space defined by weighted mean and by using s−numbers of operators from a Banach space X into a Banach space Y. We give the sufficient (not necessary) conditions on E such that the components SEX,Y≔T∈LX,Y:snTn=0∞∈E of the class SE form pre-quasi operator ideal, the class of all finite rank operators are dense in the Banach pre-quasi ideal SE, the pre-quasi operator ideal formed by the sequence of approximation numbers is strictly contained for different weights and powers, the pre-quasi Banach Operator ideal formed by the sequence of approximation numbers is small, and finally, the pre-quasi Banach operator ideal constructed by s−numbers is simple Banach space.http://dx.doi.org/10.1155/2020/9164781 |
| spellingShingle | Awad A. Bakery Afaf R. Abou Elmatty Pre-Quasi Simple Banach Operator Ideal Generated by s−Numbers Journal of Function Spaces |
| title | Pre-Quasi Simple Banach Operator Ideal Generated by s−Numbers |
| title_full | Pre-Quasi Simple Banach Operator Ideal Generated by s−Numbers |
| title_fullStr | Pre-Quasi Simple Banach Operator Ideal Generated by s−Numbers |
| title_full_unstemmed | Pre-Quasi Simple Banach Operator Ideal Generated by s−Numbers |
| title_short | Pre-Quasi Simple Banach Operator Ideal Generated by s−Numbers |
| title_sort | pre quasi simple banach operator ideal generated by s numbers |
| url | http://dx.doi.org/10.1155/2020/9164781 |
| work_keys_str_mv | AT awadabakery prequasisimplebanachoperatoridealgeneratedbysnumbers AT afafrabouelmatty prequasisimplebanachoperatoridealgeneratedbysnumbers |