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...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
|
| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2004/849723 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850160111378497536 |
|---|---|
| author | Peter G. Dodds Theresa K. Dodds Alexander A. Sedaev Fyodor A. Sukochev |
| author_facet | Peter G. Dodds Theresa K. Dodds Alexander A. Sedaev Fyodor A. Sukochev |
| author_sort | Peter G. Dodds |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b107cee295354996804eda56ef97cdff |
| institution | OA Journals |
| issn | 0972-6802 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-b107cee295354996804eda56ef97cdff2025-08-20T02:23:15ZengWileyJournal of Function Spaces and Applications0972-68022004-01-012332335610.1155/2004/849723Local Uniform Convexity and Kadec-Klee Type Properties in K-interpolation spaces IIPeter G. Dodds0Theresa K. Dodds1Alexander A. Sedaev2Fyodor A. Sukochev3School of Informatics and Engineering, Flinders University, Bedford Park, SA 5042, AustraliaSchool of Informatics and Engineering, Flinders University, Bedford Park, SA 5042, AustraliaDepartment of Mathematics, Voronezh State University of Architecture and Civil Engineering, 394006 Voronezh, 20-letiya Oktyabrya 84, RussiaSchool of Informatics and Engineering, Flinders University, Bedford Park, SA 5042, AustraliaWe 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.http://dx.doi.org/10.1155/2004/849723 |
| spellingShingle | Peter G. Dodds Theresa K. Dodds Alexander A. Sedaev Fyodor A. Sukochev Local Uniform Convexity and Kadec-Klee Type Properties in K-interpolation spaces II Journal of Function Spaces and Applications |
| title | Local Uniform Convexity and Kadec-Klee Type Properties in K-interpolation spaces II |
| title_full | Local Uniform Convexity and Kadec-Klee Type Properties in K-interpolation spaces II |
| title_fullStr | Local Uniform Convexity and Kadec-Klee Type Properties in K-interpolation spaces II |
| title_full_unstemmed | Local Uniform Convexity and Kadec-Klee Type Properties in K-interpolation spaces II |
| title_short | Local Uniform Convexity and Kadec-Klee Type Properties in K-interpolation spaces II |
| title_sort | local uniform convexity and kadec klee type properties in k interpolation spaces ii |
| url | http://dx.doi.org/10.1155/2004/849723 |
| work_keys_str_mv | AT petergdodds localuniformconvexityandkadeckleetypepropertiesinkinterpolationspacesii AT theresakdodds localuniformconvexityandkadeckleetypepropertiesinkinterpolationspacesii AT alexanderasedaev localuniformconvexityandkadeckleetypepropertiesinkinterpolationspacesii AT fyodorasukochev localuniformconvexityandkadeckleetypepropertiesinkinterpolationspacesii |