Pertubation Problems For Semi-Fredholm Operators

In this paper, we mainly study the stability of semi-Fredholm operator under the perturbation of some kinds of operators. We mainly discuss the problems of the stability of semi-Fredholm operator and its index by the methods of algebra, inequality and operator algebras.And we extend the class of operators in which the theorem of stability of semi-Fredholm operator also holds.The whole paper has three chapters altogether. The main part is the third chapter. In the third chapter, we first introduce the definition of the power compact operators and the quasi-power compact operators. Then we prove that the theorem of stability of semi-Fredholm operator and its index also holds for power compact operators. Moreover, for semi-Fredholm operators, quasi-power compact operators belong to their perturbation class.