有界线性算子的a-Browder定理及(R_(1))性质

A-Browder′s theorem and property(R_(1))for bounded linear operators

给出了有界线性算子满足a-Browder定理且具有(R_(1))性质的充要条件,研究了算子函数满足a-Browder定理且具有(R_(1))性质的判定方法,应用所得结论,给出了一类重要算子及其函数满足a-Browder定理且具有(R_(1))性质的判别定理。

In this paper,we give the necessary and sufficient conditions for bounded linear operators to hold the property(R_(1))and a-Browder's theorem.In addition,we characterize the judgements for operator functions satisfying property(R_(1))and a-Browder's theorem.As an application,a criterion theorem is given for a class of important operators and their functions to satisfy a-Browder's theorem and property(R_(1)).