On diffeomorphisms deleting weak compacta in Banach spaces
The paper deals with the question, what can be said about smooth negligibility of compacta in those Banach spaces with smooth partitions of unity? It is inspired by the following theorem of Victor Klee and related results: If X is a non-reflexive Banach space or an infinite-dimensional Lp-space and...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2004 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/49595 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/49595 |
| Access Level: | acceso abierto |
| Palabra clave: | 517.98 Diffeomorphisms in Banach spaces Weak compacta Smooth partitions of unity Análisis funcional y teoría de operadores |
| Sumario: | The paper deals with the question, what can be said about smooth negligibility of compacta in those Banach spaces with smooth partitions of unity? It is inspired by the following theorem of Victor Klee and related results: If X is a non-reflexive Banach space or an infinite-dimensional Lp-space and K is a compact subset of X there exists a homeomorphism between X and X rK which is the identity outside a given neighborhood of K. The main result of the current article now is concerned with an infinite-dimensional Banach space X which has Cp-smooth partitions of unity for some p 2 N[{1}. Then, for every starlike body A with dist(K,X rA) > 0, there exists a Cp-diffeomorphism h:X !X rK such that h is the identity outside A. |
|---|