Publication: Interpolation by Weakly Differentiable Functions on Banach-Spaces
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Publication Date
1994-03
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Academic Press
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Abstract
Let (a(n)) be a weakly null Schauder basis of a Banach space E, and let (lambda(n)) be a convergent sequence of real numbers. We study the problem of finding an m-times weakly uniformly differentiable function f on E such that f(a(n)) = lambda(n). We prove that this problem has always a solution for m = 1. In some cases we find a solution for m = infinity, for instance when E is super-reflexive or when (a(n)) is a symmetric basis and E does not contain a copy of c0. In these cases we obtain as a consequence the nonreflexivity of the space of infinitely weakly uniformly differentiable functions on E.