关于两个算子乘积的谱

ON SPECTRUM OF PRODUCT OF TWO OPERATORS

设A,B是milbert空间H上的两个有界线性算子,本文给出了AB与BA有相同的谱的充分必要条件,同时给出了对任意的A,AB与BA有相同谱的充分必要条件。另外,若B是正算子,对AB的谱话的范围作出了估计,这些结果推广和改进了[1]中的主要命题l与2。

Let A and B bc two operators on a Hilbert space H. In this notes we give a neces- sary and sufficient condition of σ(AU) =<(BA). Given B, We also get a necessary and sufficient condition so that σ(AB) =λ(BA) for any A.