The Representation Theorem of onto Isometric Mappings between Two Unit Spheres of l^1（Γ） Type Spaces and The Application to the Isometric Extension Problem

In this paper, we first derive the representation theorem of onto isometric mappings in the unit spheres of l^1（Γ） type spaces, and then conchlde that such mappings can be extended to the whole space as real linear isometries by using a previous result of the author.