On perturbations and extensions of isometric operators (Q5935720)
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scientific article; zbMATH DE number 1610930
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On perturbations and extensions of isometric operators |
scientific article; zbMATH DE number 1610930 |
Statements
On perturbations and extensions of isometric operators (English)
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25 November 2002
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Banach spaces
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nonlinear isometries
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stability
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Mazur-Ulam theorem
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surjective isometry
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isometric extension
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The reviewed paper is a short survey, rich of multiple problems and results that is concerned with the general question of stability of (nonlinear) isometries between Banach spaces or their certain parts. Some of them are connected with the classical Mazur-Ulam theorem. One of other questions is e.g. a problem of \textit{D. Tingley} [Geom. Dedicata 22, 371-378 (1987; Zbl 0615.51005)]: NEWLINENEWLINENEWLINELet \(v\) be a surjective isometry between unit spheres \(S(E)\) and \(S(F)\) of Banach spaces \(E\) and \(F\). Does \(v\) have an isometric extension?
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