Abstract:

In this paper, the author studies the extension of isometries between unit
spheres of real normed spaces. The author considers a new space E^#, which is called the positively homogeneous dual space, and studies it under a new topology σ(E^#, E). Then, the author shows that a class of surjective isometries between unit spheres of real normed spaces can be linearly isometrically extended to the whole space.

Key words: Positively homogeneous, Isometric extension, Unit sphere