Annals of Functional Analysis

Nonlinear isometries between function spaces

Kathleen Roberts and Kristopher Lee

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We demonstrate that any surjective isometry T:AB not assumed to be linear between unital, completely regular subspaces of complex-valued, continuous functions on compact Hausdorff spaces is of the form T(f)=T(0)+Re[μ(fτ)]+iIm[ν(fρ)], where μ and ν are continuous and unimodular, there exists a clopen set K with ν=μ on K and ν=μ on Kc, and τ and ρ are homeomorphisms.

Article information

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

Received: 16 July 2016
Accepted: 13 December 2016
First available in Project Euclid: 2 June 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46B04: Isometric theory of Banach spaces
Secondary: 46E25: Rings and algebras of continuous, differentiable or analytic functions {For Banach function algebras, see 46J10, 46J15}

isometry nonlinear function spaces


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

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