一类线性算子的扰动理论及其应用

<正> 离散型算子扰动理论的主要结果为Schwartz—Kramer得到,这可详见[5].[5]中是使用谱族的方法来处理的,我们将用无条件基的理论来证明这个结果(定理1.3的1)2)).显然证明较之[5]大为简化,并且免去了在Banach空间情形吋所要求的“弱完备”条件,以及得到其它一些结果(定理1.3的3)4)).

THE PERTURBATION THEORY FOR A CLASS OF LINEAR OPERATORS AND ITS APPLICATIONS

This paper discusses the perturbation theory of linear operators of discrete type by using the theory of unconditional bases. With this perturbation theory, we have given a rigorous foundation for schSdinger's perturbation theory and the recurrent formulas of revisory, terms for perturbant eigenvalues and eigenvectors. Finally, an application for the problem of elastic oscillation is provided.