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arXiv · 1907.00575

Extension of isometries from the unit sphere of a rank-2 Cartan factor

Ondřej F. K. Kalenda·Antonio M. Peralta
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Abstract

We prove that every surjective isometry from the unit sphere of a rank-2 Cartan factor $C$ onto the unit sphere of a real Banach space $Y$, admits an extension to a surjective real linear isometry from $C$ onto $Y$. The conclusion also covers the case in which $C$ is a spin factor. This result closes an open problem and, combined with the conclusion in a previous paper, allows us to establish that every JBW$^*$-triple $M$ satisfies the Mazur--Ulam property, that is, every surjective isometry from its unit sphere onto the unit sphere of a arbitrary real Banach space $Y$ admits an extension to a surjective real linear isometry from $M$ onto $Y$.

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Ondřej F. K. Kalenda, Antonio M. Peralta. 2019-07-01. Extension of isometries from the unit sphere of a rank-2 Cartan factor. https://doi.org/10.1007/s13324-020-00448-2

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