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ALMOST CONTRACTIVE RETRACTIONS IN ORLICZ SPACESGRZEGORZ LEWICKI AND GIULIO TROMBETTA Let Bk denote the Euclidean unit ball in R* equipped with the A:-dimensional Lebesgue measure and let : K + -* R + be a convex function satisfying 0(0) = 0, 0 for some t > 0. Denote by E* = E^{B k ) the Orlicz space of finite elements (see (1.6)) generated by

In this paper we consider the Wos' ko problem of evaluating, in an infinite-dimensional Banach space X, the infimum of all k ^ 1 for which there exists a fc-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.