Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8899280 | Journal of Mathematical Analysis and Applications | 2018 | 14 Pages |
Abstract
Assume that A,B are uniform algebras on compact Hausdorff spaces X and Y, respectively. Let T:AâB be a map (nonlinear in general) satisfying T(Aâ1)=Bâ1 and T1=1. We show that, if there exist constants α,βâ¥1 such that βâ1âfâ
gâ1ââ¤âTfâ
(Tg)â1ââ¤Î±âfâ
gâ1â for all fâA and gâAâ1, then there exists a homeomorphism Ï:âBââA between the Å ilov boundaries of A and B such that (αβ)â1|f(Ï(y))|â¤|(Tf)(y)|â¤Î±Î²|f(Ï(y))| for all fâA and for all yââB. In particular âA and âB are homeomorphic. Moreover we give an example which shows that the multiple αβ in the above inequality is best possible.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Yunbai Dong, Pei-Kee Lin, Bentuo Zheng,