Local uniform convexity and Kadec-Klee type properties in K-interpolation spaces I: General Theory
We present a systematic study of the interpolation of local uniform convexity and Kadec-Klee type properties in K-interpolation spaces. Using properties of the K-functional of J.Peetre, our approach is based on a detailed analysis of properties of a Banach couple and properties of a K-interpolation...
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2004/678358 |
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| 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 present a systematic study of the interpolation of local uniform convexity and Kadec-Klee type properties in K-interpolation spaces. Using properties of the K-functional of J.Peetre, our approach is based on a detailed analysis of properties of a Banach couple and properties of a K-interpolation functional which guarantee that a given K-interpolation space is locally uniformly convex, or has a Kadec-Klee property. A central motivation for our study lies in the observation that classical renorming theorems of Kadec and of Davis, Ghoussoub and Lindenstrauss have an interpolation nature. As a partiular by-product of our study, we show that the theorem of Kadec itself, that each separable Banach space admits an equivalent locally uniformly convex norm, follows directly from our approach. |
| format | Article |
| id | doaj-art-f5a6a963d16746edb7b6d4ad2e06e124 |
| institution | Kabale University |
| issn | 0972-6802 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-f5a6a963d16746edb7b6d4ad2e06e1242025-02-03T06:07:19ZengWileyJournal of Function Spaces and Applications0972-68022004-01-012212517310.1155/2004/678358Local uniform convexity and Kadec-Klee type properties in K-interpolation spaces I: General TheoryPeter 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 present a systematic study of the interpolation of local uniform convexity and Kadec-Klee type properties in K-interpolation spaces. Using properties of the K-functional of J.Peetre, our approach is based on a detailed analysis of properties of a Banach couple and properties of a K-interpolation functional which guarantee that a given K-interpolation space is locally uniformly convex, or has a Kadec-Klee property. A central motivation for our study lies in the observation that classical renorming theorems of Kadec and of Davis, Ghoussoub and Lindenstrauss have an interpolation nature. As a partiular by-product of our study, we show that the theorem of Kadec itself, that each separable Banach space admits an equivalent locally uniformly convex norm, follows directly from our approach.http://dx.doi.org/10.1155/2004/678358 |
| 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 I: General Theory Journal of Function Spaces and Applications |
| title | Local uniform convexity and Kadec-Klee type properties in K-interpolation spaces I: General Theory |
| title_full | Local uniform convexity and Kadec-Klee type properties in K-interpolation spaces I: General Theory |
| title_fullStr | Local uniform convexity and Kadec-Klee type properties in K-interpolation spaces I: General Theory |
| title_full_unstemmed | Local uniform convexity and Kadec-Klee type properties in K-interpolation spaces I: General Theory |
| title_short | Local uniform convexity and Kadec-Klee type properties in K-interpolation spaces I: General Theory |
| title_sort | local uniform convexity and kadec klee type properties in k interpolation spaces i general theory |
| url | http://dx.doi.org/10.1155/2004/678358 |
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