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On diffeomorphisms deleting weak compacta in Banach spaces



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Azagra Rueda, Daniel y Montesinos, Alejandro (2004) On diffeomorphisms deleting weak compacta in Banach spaces. Studia Mathematica , 162 (3). pp. 229-244. ISSN 0039-3223

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URL Oficial: http://journals.impan.gov.pl/sm/


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.

Tipo de documento:Artículo
Palabras clave:Diffeomorphisms in Banach spaces; Weak compacta; Smooth partitions of unity
Materias:Ciencias > Matemáticas > Análisis funcional y teoría de operadores
Código ID:12355
Depositado:07 Mar 2011 12:06
Última Modificación:06 Feb 2014 09:23

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