n this paper we consider the Wo´sko problem ([20]) of evaluating, in an infinite-dimensional Banach space X, the infimum of all k \ge 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.
CAPONETTI D, TROMBETTA A, TROMBETTA G (2005). Proper 1-ball contractive retractions in spaces of measurable functions. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 72(2), 299-315 [10.1017/S0004972700035097].
Proper 1-ball contractive retractions in spaces of measurable functions
CAPONETTI, Diana;
2005-01-01
Abstract
n this paper we consider the Wo´sko problem ([20]) of evaluating, in an infinite-dimensional Banach space X, the infimum of all k \ge 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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