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November 2017 Nonlinear isometries between function spaces
Kathleen Roberts, Kristopher Lee
Ann. Funct. Anal. 8(4): 460-472 (November 2017). DOI: 10.1215/20088752-2017-0010

Abstract

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.

Citation

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Kathleen Roberts. Kristopher Lee. "Nonlinear isometries between function spaces." Ann. Funct. Anal. 8 (4) 460 - 472, November 2017. https://doi.org/10.1215/20088752-2017-0010

Information

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

zbMATH: 06841327
MathSciNet: MR3717168
Digital Object Identifier: 10.1215/20088752-2017-0010

Subjects:
Primary: 46B04
Secondary: 46E25

Keywords: function spaces , isometry , nonlinear

Rights: Copyright © 2017 Tusi Mathematical Research Group

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Vol.8 • No. 4 • November 2017
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