Bulletin of the Belgian Mathematical Society - Simon Stevin

Function Spaces and Nonsymmetric Norm Preserving Maps

Hadis Pazandeh and Fereshteh Sady

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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.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 25, Number 5 (2018), 729-740.

Dates
First available in Project Euclid: 18 January 2019

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1547780432

Digital Object Identifier
doi:10.36045/bbms/1547780432

Mathematical Reviews number (MathSciNet)
MR3901843

Zentralblatt MATH identifier
07038549

Subjects
Primary: 47B38: Operators on function spaces (general) 46J10: Banach algebras of continuous functions, function algebras [See also 46E25]
Secondary: 47B33: Composition operators

Keywords
uniform algebras subspaces of continuous functions Choquet boundaries weighted composition operators nonsymmetric norm preserving maps

Citation

Pazandeh, Hadis; Sady, Fereshteh. Function Spaces and Nonsymmetric Norm Preserving Maps. Bull. Belg. Math. Soc. Simon Stevin 25 (2018), no. 5, 729--740. doi:10.36045/bbms/1547780432. https://projecteuclid.org/euclid.bbms/1547780432


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