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

Yuta Enami

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arXiv · 1910.07761

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

Yuta Enami

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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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Yuta Enami. 2019-10-17. Range preserving maps between the spaces of continuous functions with values in a locally convex space. https://arxiv.org/abs/1910.07761

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