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Surjective Real-Linear Uniform Isometries Between Complex Function Algebras

Journal: Sahand Communications in Mathematical Analysis (Vol.13, No. 1)

Publication Date:

Authors : ; ;

Page : 213-240

Keywords : Choquet boundary; Function algebra; Function space; Real-linear uniform isometry;

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Abstract

In this paper, we first give a description of a surjective unit-preserving real-linear uniform isometry $ T : A longrightarrow B$,  where $ A $ and $ B $ are complex function spaces on compact Hausdorff spaces $ X $ and $ Y $, respectively, whenever ${rm ER}left (A, Xright ) = {rm Ch}left (A, Xright )$ and ${rm ER}left (B, Yright ) = {rm Ch}left (B, Yright )$. Next, we give a description of $ T $ whenever $ A $ and $ B $ are complex function algebras  and $ T $ does not assume to be unit-preserving.

Last modified: 2019-04-28 14:12:06