Gómez Gil, Javier 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
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.
|Uncontrolled Keywords:||Weakly null Schauder basis of a Banach space; super-reflexive; symmetric basis|
|Subjects:||Sciences > Mathematics > Functional analysis and Operator theory|
|Deposited On:||22 Oct 2012 10:13|
|Last Modified:||28 Jan 2016 17:23|
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