Extension of isometries on unit sphere of \(L^\infty\)
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)].
scientific article; zbMATH DE number 5954246