一致Fredholm指标算子及广义(ω′)性质

Consistent Fredholm and Index Operators and Generalized Property(ω′)

本文给出了一致Fredholm指标算子的定义及判定,同时定义了Weyl型定理的一种新变化:广义(ω')性质.根据一致Fredholm指标性质定义出一种新的谱集,通过该谱集给出了Hilbert空间上有界线性算子满足广义(ω')性质的充要条件,并且研究了广义(ω')性质的摄动,还研究了算子的亚循环性和广义(ω')性质之间的关系.

In this note, we define a class operators called consistent Fredholm and index operators and give a complete characterization of this class operators, also, we define the generalized property （ω＇）, a variant of Weyl＇s theorem. By means of the new spectrum defined in view of the property of consistence in Fredholm and index, we establish for a bounded linear operator T defined on a Hilbert space the sufficient and necessary conditions for which the generalized property （ω＇） holds. We also study the stability of generalized property （ω＇） under perturbations. In addition, the relation between the generalized property （ω＇） and hypercyclicity is discussed.