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

Abstrakt

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.

Klíčová slova

• Tingley's problem
• Mazur-Ulam property
• Extension of isometries
• Rank-2 Cartan factors
• Spin factor
• 17C65
• 46A22
• 46B20
• 46B04