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
Full-text PDF
Abstract | References | Similar Articles | Additional Information
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 $F,G\in C(X,E)$.
- Razieh Sadat Ghodrat and Fereshteh Sady, Point multipliers and the Gleason-Kahane-Żelazko theorem, Banach J. Math. Anal. 11 (2017), no. 4, 864–879. MR 3708533, DOI https://doi.org/10.1215/17358787-2017-0021
- Andrew M. Gleason, A characterization of maximal ideals, J. Analyse Math. 19 (1967), 171–172. MR 213878, DOI https://doi.org/10.1007/BF02788714
- Osamu Hatori, Takeshi Miura, and Hiroyuki Takagi, Unital and multiplicatively spectrum-preserving surjections between semi-simple commutative Banach algebras are linear and multiplicative, J. Math. Anal. Appl. 326 (2007), no. 1, 281–296. MR 2277782, DOI https://doi.org/10.1016/j.jmaa.2006.02.084
- J.-P. Kahane and W. Żelazko, A characterization of maximal ideals in commutative Banach algebras, Studia Math. 29 (1968), 339–343. MR 226408, DOI https://doi.org/10.4064/sm-29-3-339-343
- S. Kowalski and Z. Słodkowski, A characterization of multiplicative linear functionals in Banach algebras, Studia Math. 67 (1980), no. 3, 215–223. MR 592387, DOI https://doi.org/10.4064/sm-67-3-215-223
Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 46E10
Retrieve articles in all journals with MSC (2010): 46E10
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
