Extension of isometries on unit sphere of \(L^\infty\). (English) Zbl 1244.46003
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 [R. Liu and L. Zhang, J. Math. Anal. Appl. 352, No. 2, 749–761 (2009; Zbl 1160.46305)].
Reviewer: Javier Merí (Granada)
