Biseparating Maps on Fréchet Function Algebras. (27th December 2012)

• Record Type: Journal Article
• Authors: Hashemi, M. S.; Honary, T. G.; Najafi Tavani, M.
• Other Names: Hudzik Henryk Academic Editor.
• Is Part Of: Journal of function spaces and applications. Volume 2012(2012)
• Publication Date: 2012-12-27
• Subjects: Function spaces -- Periodicals; 515.73
• DOI: 10.1155/2012/947080
• Languages: English
• ISSNs: 0972-6802

Abstract

Abstract : Let A and B be strongly regular normal Fréchet function algebras on compact Hausdorff spaces X and Y, respectively, such that the evaluation homomorphisms are continuous on A and B . Then, every biseparating map T : A → B is a weighted composition operator of the form T f = h · ( f ∘ φ ), where φ is a homeomorphism from Y onto X and h is a nonvanishing element of B . In particular, T is automatically continuous.