Range preserving maps between the spaces of continuous functions with values in a locally convex space

Enami, Yuta

doi:10.1090/proc/15108

Range preserving maps between the spaces of continuous functions with values in a locally convex space
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Proc. Amer. Math. Soc. 149 (2021), 189-197 Request permission

Abstract:

Let $C(X,E)$ be the linear space of all continuous functions on a compact Hausdorff space $X$ with values in a locally convex space $E$. We characterize maps $T:C(X,E)\to C(Y,E)$ which satisfy $\mathrm {Ran}(TF-TG)\subset \mathrm {Ran}(F-G)$ for all $F,G\in C(X,E)$.

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