Extension of isometries between the unit spheres of complex lp(Γ)(p>1)spaces

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