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arXiv · 1808.01460

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

Julio Becerra-Guerrero·María Cueto-Avellaneda·Francisco J. Fernández-Polo·Antonio M. Peralta
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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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Julio Becerra-Guerrero, María Cueto-Avellaneda, Francisco J. Fernández-Polo, Antonio M. Peralta. 2018-08-04. On the extension of isometries between the unit spheres of a JBW$^*$-triple and a Banach space. https://arxiv.org/abs/1808.01460

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