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ON THE EXTENSION OF ISOMETRIES BETWEEN THE UNIT SPHERES OF A
$\text{JBW}^{\ast }$-TRIPLE AND A BANACH SPACE
- Part of
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- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 20 / Issue 1 / January 2021
- Published online by Cambridge University Press:
- 15 April 2019, pp. 277-303
- Print publication:
- January 2021
-
- Article
- Export citation
-
We prove that if
$M$ is a 
$\text{JBW}^{\ast }$-triple and not a Cartan factor of rank two, then 
$M$ satisfies the Mazur–Ulam property, that is, every surjective isometry from the unit sphere of 
$M$ onto the unit sphere of another real Banach space 
$Y$ extends to a surjective real linear isometry from 
$M$ onto 
$Y$.
