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.
Qiao Fen JIANG Huai Jie ZHONG School of Mathematics and Computer Science,Fujian Normal University, Fuzhou 350007,P.R.China.
Semi-Regular Operators and Generalized Kato Decomposition. Acta Mathematica Sinica, Chinese Series, 2009(04): 69-78 https://doi.org/10.12386/A2009sxxb0085