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


Author: Yuta Enami
Journal: Proc. Amer. Math. Soc. 149 (2021), 189-197
MSC (2010): Primary 46E10
DOI: https://doi.org/10.1090/proc/15108
Published electronically: October 9, 2020
MathSciNet review: 4172596
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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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Additional Information

Yuta Enami
Affiliation: Department of Mathematical Science, Faculty of Fundamental Scineces, Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan
ORCID: 0000-0003-4296-7212
Email: enami@m.sc.niigata-u.ac.jp

Keywords: Range preserving map, vector-valued function space
Received by editor(s): October 29, 2019
Received by editor(s) in revised form: March 1, 2020, March 12, 2020, and March 17, 2020
Published electronically: October 9, 2020
Communicated by: Professor Stephen Dilworth
Article copyright: © Copyright 2020 American Mathematical Society