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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Characterizations of isometric isomorphisms between uniform algebras via nonlinear range-preserving properties


Authors: Osamu Hatori, Takeshi Miura and Hiroyuki Takagi
Journal: Proc. Amer. Math. Soc. 134 (2006), 2923-2930
MSC (2000): Primary 46J10, 47B48
Published electronically: April 11, 2006
MathSciNet review: 2231616
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Abstract: Let $ T$ be a surjective mapping from a uniform algebra $ A$ on a compact Hausdorff space $ X$ onto a uniform algebra on a compact Hausdorff space $ Y$. Suppose that $ fg(X)=T(f)T(g)(Y)$ holds for every $ f,g\in A$. Then we have that $ T$ is an almost isometric isomorphism, which is a generalization of results of Molnár (2002) and Rao and Roy (2005).


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Additional Information

Osamu Hatori
Affiliation: Department of Mathematics, Faculty of Science, Niigata University, Niigata 950-2181, Japan
Email: hatori@math.sc.niigata-u.ac.jp

Takeshi Miura
Affiliation: Department of Basic Technology, Applied Mathematics and Physics, Yamagarta University, Yonezawa 992-8510, Japan
Email: miura@yz.yamagata-u.ac.jp

Hiroyuki Takagi
Affiliation: Department of Mathematical Sciences, Faculty of Science, Shinshu University, Matsumoto 390-8621, Japan
Email: takagi@math.shinshu-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08500-5
PII: S 0002-9939(06)08500-5
Keywords: Uniform algebras, isometric isomorphisms, spectrum preserving map
Received by editor(s): April 22, 2005
Published electronically: April 11, 2006
Additional Notes: The authors were partially supported by the Grants-in-Aid for Scientific Research, The Ministry of Education, Science, Sports and Culture, Japan.
Dedicated: Dedicated to Professor Sin-Ei Takahasi on his sixtieth birthday
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2006 American Mathematical Society