Tingley's problem through the facial structure of an atomic JBW*-triple

TL;DR

This paper proves that surjective isometries between unit spheres of atomic JBW*-triples extend to linear isometries, providing a new solution to Tingley's problem in the Jordan algebra context.

Contribution

It establishes that such isometries can be extended linearly, advancing the understanding of geometric structure in atomic JBW*-triples.

Findings

Surjective isometries extend to linear isometries.

New solution to Tingley's problem in Jordan setting.

Advances geometric understanding of atomic JBW*-triples.

Abstract

We prove that every surjective isometry between the unit spheres of two atomic JBW$^*$-triples $E$ and $B$ admits a unit extension to a surjective real linear isometry from $E$ into $B$. This result constitutes a new positive answer to Tignley's problem in the Jordan setting.