EXTENSION OF ISOMETRIES BETWEEN THE UNIT SPHERES OF COMPLEX lp(Γ)(p 1) SPACES

摘要

In this paper, we study the extension of isometries between the unit spheres of complex Banach spaces lp(Γ) and lp(△)(p > 1). We first derive the representation of isometries between the unit spheres of complex Banach spaces lp(Γ) and lp(△). Then we arrive at a conclusion that any surjective isometry between the unit spheres of complex Banach spaces lp(Γ)and lp(△) can be extended to be a linear isometry on the whole space.