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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/325141 |
| Summary: | 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. |
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| ISSN: | 0972-6802 1758-4965 |