Local Uniform Convexity and Kadec-Klee Type Properties in K-interpolation spaces II
We study local uniform convexity and Kadec-Klee type properties in K-interpolation spaces of Lorentz couples. We show that a wide class of Banach couples of (commutative and) non-commutative Lorentz spaces possess the (so-alled) (DGL)-property originally introduced by Davis, Ghoussoub and Lindenstra...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2004/849723 |
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| Summary: | We study local uniform convexity and Kadec-Klee type properties in K-interpolation spaces of Lorentz couples. We show that a wide class of Banach couples of (commutative and) non-commutative Lorentz spaces possess the (so-alled) (DGL)-property originally introduced by Davis, Ghoussoub and Lindenstrauss in the context of renorming order continuous Banach latties. This property is used as a key tool to show that local uniform convexity and certain Kadec-Klee type properties in non-commutative symmetric spaces of measurable operators may be inferred from corresponding properties of the parameter space of the K-interpolation method. Further applications are given to renorming properties of separable symmetric Banach function spaces and their non-commutative counterparts. |
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| ISSN: | 0972-6802 |