## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Function Spaces and Nonsymmetric Norm Preserving Maps

#### 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

https://projecteuclid.org/euclid.bbms/1547780432

Digital Object Identifier
doi:10.36045/bbms/1547780432

Mathematical Reviews number (MathSciNet)
MR3901843

Zentralblatt MATH identifier
07038549

#### 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