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Interpolation by Weakly Differentiable Functions on Banach-Spaces

Gómez, J. and Jaramillo Aguado, Jesús Ángel (1994) Interpolation by Weakly Differentiable Functions on Banach-Spaces. Journal of Mathematical Analysis and Applications, 182 (2). pp. 501-515. ISSN 0022-247X

Official URL: http://www.sciencedirect.com/science/article/pii/S0022247X84711000

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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.

Item Type:Article
Uncontrolled Keywords:Weakly null Schauder basis of a Banach space; super-reflexive; symmetric basis
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:16786
Deposited On:22 Oct 2012 10:13
Last Modified:22 Oct 2012 10:13

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