On a classical renorming construction of V. Klee
We further develop a classical geometric construction of V. Klee and show, typically, that if X is a nonreflexive Banach space with separable dual, then X admits an equivalent norm vertical bar . vertical bar which is Frechet differentiable, locally uniformly rotund, its dual norm vertical bar . ver...
| Authors: | , , |
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| Format: | article |
| Publication Date: | 2012 |
| Country: | España |
| Institution: | Universitat Politècnica de València (UPV) |
| Repository: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Language: | English |
| OAI Identifier: | oai:riunet.upv.es:10251/31402 |
| Online Access: | https://riunet.upv.es/handle/10251/31402 |
| Access Level: | Open access |
| Keyword: | Rotund norm Locally uniformly rotund norm Gateaux differentiable norm Frechet differentiable norm Renormings MATEMATICA APLICADA |
| Summary: | We further develop a classical geometric construction of V. Klee and show, typically, that if X is a nonreflexive Banach space with separable dual, then X admits an equivalent norm vertical bar . vertical bar which is Frechet differentiable, locally uniformly rotund, its dual norm vertical bar . vertical bar* is uniformly Gateaux differentiable, the weak* and the norm topologies coincide on the sphere of (X*, vertical bar . vertical bar*) and, yet, vertical bar . vertical bar* is not rotund. This proves (a stronger form of) a conjecture of V. Klee. (C) 2011 Elsevier Inc. |
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