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 comple...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.展开更多
基金supported by Higher Educational Science and Technology Program Foundation of Shandong Province(J11LA02)Young and Middle-Aged Scientists Research Foundation of Shandong Province(BS2010SF004)Higher Educational Science and Technology Program Foundation of Shandong Province(J10LA53)
文摘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.
