Tingley's problem on uniform algebras

Abstract

We prove that a surjective isometry between the unit spheres of two uniform algebras is extended to a surjective real-linear isometry between the uniform algebras. It provides the first positive solution for Tingley's problem on a Banach space of analytic functions.

arXiv comment19 pages

References in corpus (3)

• Tingley's problem through the facial structure of operator algebras
• A solution to Tingley's problem for isometries between the unit spheres of compact C${}^{\ast }$-algebras and JB${}^{\ast }$-triples
• Extension of isometries from the unit sphere of a rank-2 Cartan factor