Hilbert空间中单位球内的等距变换群及Mbius变换分类

Isometric groups in unit ball of Hilbert spaces and classification of Mbius transformations

在Hilbert空间中,定义单位球内的非欧度量,并且证明了所有保持单位球B不变的等距变换M(B)恰好是这个度量下的等距同构群.最后对Hilbert空间中Mbius变换给出了完整的分类.

We introduce the definition of the non-Euclidean metric in unit ball of Hilbert space, and prove that M（B） ,the group of Moebius transformations keeping the unit ball, is exactly the isometric group with respect to this metric. Finally we give a complete distribution of Moebius transformations in Hilbert space.