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december 2018 Function Spaces and Nonsymmetric Norm Preserving Maps
Hadis Pazandeh, Fereshteh Sady
Bull. Belg. Math. Soc. Simon Stevin 25(5): 729-740 (december 2018). DOI: 10.36045/bbms/1547780432

Abstract

Let $X,Y$ be compact Hausdorff spaces and $A,B$ be either closed subspaces of $C(X)$ and $C(Y)$, respectively, containing constants or positive cones of such subspaces. In this paper we study surjections $T:A \longrightarrow B$ satisfying the norm condition $\|T(f) T(g) -1 \|_Y=\|fg-1\|_X$ for all $f,g \in A$, where $\|\cdot\|_X$ and $\|\cdot\|_Y$ denote the supremum norms. We show that under a mild condition on the strong boundary points of $A$ and $B$ (and the assumption $T(i)=i T(1)$ in the subspace case), the map $T$ is a weighted composition operator on the set of strong boundary points of $B$. This result is an improvement of the known results for uniform algebra case to closed linear subspaces and their positive cones.

Citation

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Hadis Pazandeh. Fereshteh Sady. "Function Spaces and Nonsymmetric Norm Preserving Maps." Bull. Belg. Math. Soc. Simon Stevin 25 (5) 729 - 740, december 2018. https://doi.org/10.36045/bbms/1547780432

Information

Published: december 2018
First available in Project Euclid: 18 January 2019

zbMATH: 07038549
MathSciNet: MR3901843
Digital Object Identifier: 10.36045/bbms/1547780432

Subjects:
Primary: 46J10, 47B38
Secondary: 47B33

Rights: Copyright © 2018 The Belgian Mathematical Society

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Vol.25 • No. 5 • december 2018
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