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

Bulletin of the Australian Mathematical Society Bull. Austral. Math. Soc. 0004-9727 ALNBAB 2005 72 2 10.wxyz/CV72P2 http://www.austms.org.au/Publ/Bulletin/V72P2/ Proper $1$-ball contractive retractions in Banach spaces of measurable functions D. Caponetti A. Trombetta G. Trombetta 14 February 2006 2006 2 14 299 315 722-5138-CaTrTr-2005 10.wxyz/C2005V72P2p299 http://www.austms.org.au/Publ/Bulletin/V72P2/722-5138-CaTrTr/ In this paper we consider the Wo\'sko problem 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. 47H09, 46E30 MR2183411 02246392 J. Appell, N.A. Erkazova, S. Falcon Santana and M. 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