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On diffeomorphisms deleting weak compacta in Banach spaces

Azagra Rueda, Daniel and 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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Abstract

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.


Item Type:Article
Uncontrolled Keywords:Diffeomorphisms in Banach spaces; Weak compacta; Smooth partitions of unity
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:12355
Deposited On:07 Mar 2011 12:06
Last Modified:06 Feb 2014 09:23

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