半正则算子与广义Kato分解

Semi-Regular Operators and Generalized Kato Decomposition

给出了半正则算子的乘积仍是半正则的一个充分条件,得到了半正则算子的解析核与拟幂零部分在可交换的小范数摄动下的稳定性,证明了广义Kato谱与半正则谱相差至多可数个孤立点,并利用这个结论证明了算子的解析核与拟幂零部分在其广义Kato预解集的连通分支中的稳定性.

In this paper, a sufficient condition which makes the product of two semiregular operators be semi-regular is presented. We obtain the stablities of analytical core and quasi-nilpotent part of semi-regular operators under small communicative perturbations. We get that the generalized Kato spectrum and the semi-regular spectrum differ of at most countably many isolated points; By means of this result, we show the stablities of analytical core and quasi-nilpotent part on a component of the generalized Kato resolvent set of a bounded operator.