算子函数的a-Weyl定理和(\mathcalR )性质

a-Weyl's Theorem and Property(\mathcalR ) for Operator Functions

摘要: 文章利用谱集的关系给出判定有界线性算子分别满足a-Weyl定理和(\mathcalR )性质的新方法, 在此基础上, 得到算子同时满足a-Weyl定理和(\mathcalR )性质的充要条件；然后，讨论了算子函数满足a-Weyl定理和(\mathcalR )性质的充要条件, 最终得到算子函数同时满足a-Weyl定理和(\mathcalR )性质的判定方法。

Abstract: The new judgements for which a-Weyl's theorem, property (\mathcalR ), both a-Weyl's theorem and property (\mathcalR ) hold are given. In additional, the necessary and sufficient conditions for operator functions to satisfy the a-Weyl's theorem, the property (\mathcalR ), both the a-Weyl's theorem and the property (\mathcalR ) are considered.