Operators on C_{0}(L,X) whose range does not contain c_{0}
Functional Analysis
2008-01-16 v1
Abstract
This paper contains the following results: a) Suppose that X is a non-trivial Banach space and L is a non-empty locally compact Hausdorff space without any isolated points. Then each linear operator T: C_{0}(L,X)\to C_{0}(L,X), whose range does not contain C_{00} isomorphically, satisfies the Daugavet equality ||I+T||=1+||T||. b) Let \Gamma be a non-empty set and X, Y be Banach spaces such that X is reflexive and Y does not contain c_{0} isomorphically. Then any continuous linear operator T: c_{0}(\Gamma,X)\to Y is weakly compact.
Cite
@article{arxiv.0801.2314,
title = {Operators on C_{0}(L,X) whose range does not contain c_{0}},
author = {Jarno Talponen},
journal= {arXiv preprint arXiv:0801.2314},
year = {2008}
}