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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: Linear function spaces and their duals Topological linear spaces and related structures Special classes of linear operators Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  15 April 2019

Julio Becerra-Guerrero Open the ORCID record for Julio Becerra-Guerrero [Opens in a new window] ,
María Cueto-Avellaneda Open the ORCID record for María Cueto-Avellaneda [Opens in a new window] ,
Francisco J. Fernández-Polo Open the ORCID record for Francisco J. Fernández-Polo [Opens in a new window]  and
Antonio M. Peralta Open the ORCID record for Antonio M. Peralta [Opens in a new window]
Julio Becerra-Guerrero
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071Granada, Spain ([email protected]; [email protected]; [email protected]; [email protected])
María Cueto-Avellaneda
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071Granada, Spain ([email protected]; [email protected]; [email protected]; [email protected])
Francisco J. Fernández-Polo
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071Granada, Spain ([email protected]; [email protected]; [email protected]; [email protected])
Antonio M. Peralta
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071Granada, Spain ([email protected]; [email protected]; [email protected]; [email protected])
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Abstract

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 $Y$.

Keywords

Tingley’s problemMazur–Ulam propertyextension of isometriesJBW∗ -triples

MSC classification

Primary: 47B49: Transformers, preservers (operators on spaces of operators)
Secondary: 46A22: Theorems of Hahn-Banach type; extension and lifting of functionals and operators 46B20: Geometry and structure of normed linear spaces 46B04: Isometric theory of Banach spaces 46A16: Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) 46E40: Spaces of vector- and operator-valued functions
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 20 , Issue 1 , January 2021 , pp. 277 - 303
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Copyright
© Cambridge University Press 2019

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