A Note on Generalized Approximation Property
We introduce a notion of generalized approximation property, which we refer to as --AP possessed by a Banach space , corresponding to an arbitrary Banach sequence space and a convex subset of , the class of bounded linear operators on . This property includes approximation property studied by Grot...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/325141 |
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| _version_ | 1832568403459571712 |
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| author | Antara Bhar Manjul Gupta |
| author_facet | Antara Bhar Manjul Gupta |
| author_sort | Antara Bhar |
| collection | DOAJ |
| description | We introduce a notion of generalized approximation property, which we refer to as --AP possessed by a Banach space , corresponding to an arbitrary Banach sequence space and a convex subset of , the class of bounded linear operators on . This property includes approximation property studied by Grothendieck, -approximation property considered by Sinha and Karn and Delgado et al., and also approximation property studied by Lissitsin et al. We characterize a Banach space having --AP with the help of -compact operators, -nuclear operators, and quasi--nuclear operators. A particular case for () has also been characterized. |
| format | Article |
| id | doaj-art-058eb6cc9c0c469b9c634a21426a56cb |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-058eb6cc9c0c469b9c634a21426a56cb2025-02-03T00:59:04ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/325141325141A Note on Generalized Approximation PropertyAntara Bhar0Manjul Gupta1Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur 208016, IndiaDepartment of Mathematics and Statistics, Indian Institute of Technology, Kanpur 208016, IndiaWe introduce a notion of generalized approximation property, which we refer to as --AP possessed by a Banach space , corresponding to an arbitrary Banach sequence space and a convex subset of , the class of bounded linear operators on . This property includes approximation property studied by Grothendieck, -approximation property considered by Sinha and Karn and Delgado et al., and also approximation property studied by Lissitsin et al. We characterize a Banach space having --AP with the help of -compact operators, -nuclear operators, and quasi--nuclear operators. A particular case for () has also been characterized.http://dx.doi.org/10.1155/2013/325141 |
| spellingShingle | Antara Bhar Manjul Gupta A Note on Generalized Approximation Property Journal of Function Spaces and Applications |
| title | A Note on Generalized Approximation Property |
| title_full | A Note on Generalized Approximation Property |
| title_fullStr | A Note on Generalized Approximation Property |
| title_full_unstemmed | A Note on Generalized Approximation Property |
| title_short | A Note on Generalized Approximation Property |
| title_sort | note on generalized approximation property |
| url | http://dx.doi.org/10.1155/2013/325141 |
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