Impacto
Azagra Rueda, Daniel and Montesinos, Alejandro (2004) On diffeomorphisms deleting weak compacta in Banach spaces. Studia Mathematica , 162 (3). pp. 229244. ISSN 00393223

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Official URL: http://journals.impan.gov.pl/sm/
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 nonreflexive Banach space or an infinitedimensional Lpspace 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 infinitedimensional Banach space X which has Cpsmooth partitions of unity for some p 2 N[{1}. Then, for every starlike body A with dist(K,X rA) > 0, there exists a Cpdiffeomorphism 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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