L^p空间单位球面上的等距线性延拓

Extension of Isometries on the Unit Sphere of L^p Space

对L^p空间单位球面上的Tingley问题进行了研究,证明了:从L^p(Ω,μ)(1<p<∞,p≠2)空间单位球面到任意巴拿赫空间单位球面间的满等距映射一定可以(实)线性延拓到整个空间上去.

In this paper, the author prove that every isometry from the unit sphere of Lp space（1〈P〈∞,P≠2）） onto the unit sphere of a Banach space E can be extended to be a linear isometry of Lp onto E.