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Journal of Function Spaces and Applications
Volume 2012 (2012), Article ID 947080, 7 pages
doi:10.1155/2012/947080
Biseparating Maps on Fréchet Function Algebras
1Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran 14778-93855, Iran
2Department of Mathematics, Islamic Azad University, Islamshahr Branch, Tehran 33147-67653, Iran
Received 20 August 2012; Accepted 13 November 2012
Academic Editor: Henryk Hudzik
Copyright © 2012 M. S. Hashemi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Let and be strongly regular normal Fréchet function algebras on compact Hausdorff spaces and , respectively, such that the evaluation homomorphisms are continuous on and . Then, every biseparating map is a weighted composition operator of the form , where is a homeomorphism from onto and is a nonvanishing element of . In particular, is automatically continuous.