关于正算子的n次方根

The n-th Root of a Positive Operator

本文首先给出复的Hilbert空间上正算子n次方根存在唯一性的构造性证明.然后讨论了关于一个正算子T的n次方根序列{T^(1/n))的极限的三种结果.

For a positive operator T on the complex Hilbert space H, this paper first gives a constructive proof of tile existence and uniquence of its n-th root of T, and then discusses some results about the limit of tile sequence{m√T}