On the extension of isometries between the unit spheres of a JBW^*-triple and a Banach space

2018/08/04 by Becerra-Guerrero, Julio, Cueto-Avellaneda, María, Fernández-Polo, Francisco J. +1
#FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1808.01460

Abstract

We prove that every JBW^*-triple M with rank one or rank bigger than or equal to three satisfies the Mazur--Ulam property, that is, every surjective isometry from the unit sphere of M onto the unit sphere of another Banach space Y extends to a surjective real linear isometry from M onto Y. We also show that the same conclusion holds if M is not a JBW^*-triple factor, or more generally, if the atomic part of M^** is not a rank two Cartan factor.

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