一致可逆性质及广义(ω)性质的摄动

Consistent Invertibility and Perturbations of the Generalized Property(ω)

Hilbert空间算子T∈B(H)称为是一致可逆的,若对任意的S∈B(H),TS与ST的可逆性相同.本文中根据一致可逆性质定义了一个新的谱集,用该谱集来研究广义(ω)性质的稳定性,即考虑了Hilbert空间上有界线性算子的有限秩摄动、幂零摄动以及Riesz摄动的广义(ω)性质.之后研究了能分解成有限个正规算子乘积的一类算子的广义(ω)性质的稳定性.

A Hilbert space operator T∈B（H） may be said to be ＂consistent in invertibility＂ provided that for each S∈B（H）,TS and ST are either both or neither invertible.The induced spectrum contributes the stability of generalized property（ω）, for a bounded operator T acting on a Hilbert space,under perturbations by finite rank operators,by nilpotent operators and quisi-nilpotent operators commuting with T.The stability of generalized property（ω） of the operators which are the products of finitely normal operators are considered.