小紧扰动下三角算子有唯一的强不可约分解

Triangular Operators Being of Unique Strongly Irreducible Decomposition Under Small Compact Perturbation

作用在 Hilbert空间 H上的有界线性算子 T称为强不可约的 ,如果 T不与任何非平凡的幂等算子可交换 。

A bounded linear operator T acting on Hilbert space H is considered to be strongly irreducible if T does not commute any idempotent operator. It is proven that certain triangular operators have unique strongly irreducible decomposition under small compact perturbation.