On extension of isometries between unit spheres of AL~p-spaces (0 < p <)

Abstract

In this paper, we study the extension of isometries between unit spheres of atomic AL p -spaces (0 < p < ∞, p ¬= 2). We find a condition under which an isometry T between unit spheres can be linearly isometrically extended. Moreover, we prove that every onto isometry between unit spheres of atomic AL p -spaces (0 < p < ∞, p ¬= 2) can be linearly isometrically extended to the whole space.