Weak Compactness of Almost Limited Operators
This paper is devoted to the relationship between almost limited operators and weakly compact operators. We show that if F is a σ-Dedekind complete Banach lattice, then every almost limited operator T:E→F is weakly compact if and only if E is reflexive or the norm of F is order continuous. Also, we...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2014-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2014/263159 |
| Summary: | This paper is devoted to the relationship between almost limited operators and weakly compact operators. We show that if F is a σ-Dedekind complete Banach lattice, then every almost limited operator T:E→F is weakly compact if and only if E is reflexive or the norm of F is order continuous. Also, we show that if E is a σ-Dedekind complete Banach lattice, then the square of every positive almost limited operator T:E→E is weakly compact if and only if the norm of E is order continuous. |
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| ISSN: | 2314-8896 2314-8888 |