(ω)性质及Weyl型定理

Property (ω) and Weyl Type Theorem

(ω)性质是Rakocevic给出的Weyl定理的一种变化.本文通过定义新的谱集,给出了有界线性算子同时满足(ω)性质和a-Weyl定理的充要条件.同时,利用所得的主要结论,研究了H(p)算子的(ω)性质.

Abstract In this note we study the property （ω）, a variant of Weyl＇s theorem introduced by Rakocevic, by means the new spectrum. We establish for a bounded linear operator defined on a Banach space a sufficient and necessary condition for which both property （ω） and a-Weyl＇s theorem hold. As a consequence of the main result, we study the property （ω） and a-Weyl＇s theorem for H（p） operators.