On extension of isometries between unit spheres of L∞ and E

Abstract

In this paper, we study the extension of isometries between the unit spheres of L∞ and a normed space E. We find a condition under which an isometric mapping between the unit spheres can be extended to a linear isometry on the whole space L∞ .

Keywords: Isometric mapping, unit sphere, L∞

Quaestiones Mathematicae 31(2008), 209–218