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.

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

D. CAPONETTI;TROMBETTA A;G. TROMBETTA
2005-01-01

Abstract

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/150512
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