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SMOOTH LIPSCHITZ RETRACTIONS OF STARLIKE BODIES ONTO THEIR BOUNDARIES IN INFINITE-DIMENSIONAL BANACH SPACES

Published online by Cambridge University Press:  25 July 2001

DANIEL AZAGRA  and
MANUEL CEPEDELLO BOISO
DANIEL AZAGRA
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas, Universidad Complutense, 28040 Madrid, Spain Equipe d'Analyse, 4, place Jussieu, 75005 Paris, France; [email protected]
MANUEL CEPEDELLO BOISO
Affiliation:
Departamento de Análisis Matemático, Universidad de Sevilla, Sevilla, Spain; [email protected]
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Abstract

Let X be an infinite-dimensional Banach space, and let A be a Cp Lipschitz bounded starlike body (for instance the unit ball of a smooth norm). We prove that:

(1) the boundary ∂A is Cp Lipschitz contractible;

(2) there is a Cp Lipschitz retraction from A onto ∂A;

(3) there is a Cp Lipschitz map T : A → A with no approximate fixed points.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 4 , July 2001 , pp. 443 - 453
Copyright
© The London Mathematical Society 2001

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