多面体空间上的保正交算子

The Preserving Orthogonal Operators on Polyhedral Space

摘要: 本文主要研究多面体空间上保正交算子的性质。我们证明了二维多面体空间的单位球面上的保正交算子是一个满等距，且可以把二维多面体空间的单位球面映成二维多面体空间的单位球面，进而可以延拓到全空间等距。

Abstract: In this paper, we research the properties of preserving orthogonal operators on polyhedral space. We proved that the orthogonality-preserving operator on the unit sphere of a two-dimensional polyhedron space is a surjective isometry, and the unit sphere of a two-dimensional polyhedron space can be mapped into a unit sphere of a two-dimensional polyhedron space, and then the surjective isometry can be extended to a linear isometry on the whole space.