An Isomorphic Characterization of Property (β) of Rolewicz

Abstract

In the paper it is shown that in a Banach space with a basis there is a norm with property (β) of S. Rolewicz if and only if there is a norm which is simultaneously nearly uniformly convex and nearly uniformly smooth. The Kuratowski measure of noncompactness of a set A in a Banach space is the infimum α(A) of those ǫ > 0 for which there is a covering of A… (More)

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