RT Journal Article
T1 Interpolation by Weakly Differentiable Functions on Banach-Spaces
A1 Gómez Gil, Javier
A1 Jaramillo Aguado, Jesús Ángel
AB 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.
PB Academic Press
SN 0022-247X
YR 1994
FD 1994-03
LK https://hdl.handle.net/20.500.14352/57613
UL https://hdl.handle.net/20.500.14352/57613
DS Docta Complutense
RD 3 may 2024