赋范空间E和l^1(Γ)的单位球面间等距映射的延拓

Extension of Isometries Between Unit Spheres of Normed Space E and l^1(Γ)

研究赋范空间E和l^1(Γ)的单位球面之间的等距映射的延拓,得到E和l^1(Γ)的单位球面之间的满等距映射可以延拓为全空间E上的实线性等距算子,从而肯定地回答了相应的Tingley问题.

We study the extension of isometries between the unit spheres of normed space E and l^1（Г）. We obtain that any surjective isometry between the unit spheres of normed space E and l^1（Г） can be extended to be a linear isometry on the whole space E, and give an affirmative answer to the corresponding Tingley＇s problem.