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

Yuta Enami

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

Functional Analysis 2019-10-18 v1

Authors: Yuta Enami

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 $F,G\in C(X,E)$ .

Keywords

range preserving maps continuous functions locally convex space compact Hausdorff space linear space

Cite

@article{arxiv.1910.07761,
  title  = {Range preserving maps between the spaces of continuous functions with values in a locally convex space},
  author = {Yuta Enami},
  journal= {arXiv preprint arXiv:1910.07761},
  year   = {2019}
}

Comments

10 pages

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