相似不变子空间和保相似线性映射

Similarity-Invariant Subspaces and Similarity-Preserving Linear Maps

本文给出了可分无限维Hilbert空间H上有界线性算子全体B(H)中的相似不变子空间的构造,同时给出了B(H)上双边保相似线性映射的表示.

In this paper, the similarity-invariant subspaces of B(H), which is the Banach algebra of all bounded linear operators on a separable infinite dimensional Hilbert space H, are completely characterized and the representations of bounded linear maps on B(H) which preserve similarity in both directions are given.