## Annals of Functional Analysis

### Nonlinear isometries between function spaces

#### Abstract

We demonstrate that any surjective isometry $T\colon \mathcal{A}\to \mathcal{B}$ not assumed to be linear between unital, completely regular subspaces of complex-valued, continuous functions on compact Hausdorff spaces is of the form $\begin{equation*}T(f)=T(0)+\operatorname{Re}[\mu \cdot(f\circ\tau)]+i\operatorname{Im}[\nu \cdot(f\circ\rho)],\end{equation*}$ where $\mu$ and $\nu$ are continuous and unimodular, there exists a clopen set $K$ with $\nu=\mu$ on $K$ and $\nu=-\mu$ on $K^{c}$, and $\tau$ and $\rho$ are homeomorphisms.

#### Article information

Source
Ann. Funct. Anal. Volume 8, Number 4 (2017), 460-472.

Dates
Accepted: 13 December 2016
First available in Project Euclid: 2 June 2017

https://projecteuclid.org/euclid.afa/1496368961

Digital Object Identifier
doi:10.1215/20088752-2017-0010

Keywords
isometry nonlinear function spaces

#### Citation

Roberts, Kathleen; Lee, Kristopher. Nonlinear isometries between function spaces. Ann. Funct. Anal. 8 (2017), no. 4, 460--472. doi:10.1215/20088752-2017-0010. https://projecteuclid.org/euclid.afa/1496368961

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