摘要
Let X and Y be real Banach spaces.Suppose that the subset sm[S1(X)] of the smooth points of the unit sphere [S1(X)] is dense in S1(X).If T0 is a surjective 1-Lipschitz mapping between two unit spheres,then,under some condition,T0 can be extended to a linear isometry on the whole space.
Let X and Y be real Banach spaces.Suppose that the subset sm[S1（X）] of the smooth points of the unit sphere [S1（X）] is dense in S1（X）.If T0 is a surjective 1-Lipschitz mapping between two unit spheres,then,under some condition,T0 can be extended to a linear isometry on the whole space.
基金
supported by National Natural Science Foundation of China (Grant No.10871101)
the Research Fund for the Doctoral Program of Higher Education (Grant No. 20060055010)
