Extension of isometries on unit sphere of \(L^\infty\) (Q717741)
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scientific article; zbMATH DE number 5954246
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Extension of isometries on unit sphere of \(L^\infty\) |
scientific article; zbMATH DE number 5954246 |
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Extension of isometries on unit sphere of \(L^\infty\) (English)
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5 October 2011
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The author gives a simple proof of the fact that every surjective isometry from the unit sphere of \(L^\infty\) to the unit sphere of a Banach space can be extended to be a linear isometry on the whole space \(L^\infty\). As the author explains this result can be deduced from Theorem~3.11 in [\textit{R. Liu} and \textit{L. Zhang}, J. Math. Anal. Appl. 352, No. 2, 749--761 (2009; Zbl 1160.46305)].
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extension of isometries
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Tingley's problem
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