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arXiv · 0801.2314

Operators on C_{0}(L,X) whose range does not contain c_{0}

Jarno Talponen
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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 Γbe 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}(Γ,X)\to Y is weakly compact.

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Jarno Talponen. 2008-01-15. Operators on C_{0}(L,X) whose range does not contain c_{0}. https://arxiv.org/abs/0801.2314

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