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Proper 1-ball contractive retractions in Banach spaces of measurable functions

Published online by Cambridge University Press:  17 April 2009

D. Caponetti ,
A. Trombetta  and
G. Trombetta
D. Caponetti
Affiliation:
Department of Mathematics, University of Palermo, Via Archirafi, 34, 90123 Palermo, Italy e-mail: d.caponetti@math.unipa.it
A. Trombetta
Affiliation:
Department of Mathematics, University of Calabria, 87036 Arcavacata di Rende (CS), Italy e-mail: aletromb@unical.it
G. Trombetta
Affiliation:
Department of Mathematics, University of Calabria, 87036 Arcavacata di Rende (CS), Italy e-mail: trombetta@unical.it
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In this paper we consider the Wośko problem of evaluating, in an infinite-dimensional Banach space X, the infimum of all k ≤ 1 for which there exists a k-ball contractive retraction of the unit ball onto its boundary. We prove that in some classical Banach spaces the best possible value 1 is attained. Moreover we give estimates of the lower H-measure of noncompactness of the retractions we construct.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 72 , Issue 2 , October 2005 , pp. 299 - 315
Copyright
Copyright © Australian Mathematical Society 2005

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