联合Browder本质谱与初等算子的Browder本质谱表示

JOINT BROWDER ESSENTIAL SPECTRUM AND AN EXPRESSION OF BROWDER ESSENTIAL SPECTRUM OF ELEMENTARY OPERATORS

近来,关于算子组的各类联合谱、联合本质谱的研究已获得了一些出色成果。本文将在这些成果的基础上,讨论一类由 Snow 首先定义的,算子组的联合 Browder 本质谱及有关性质。第一节讨论联合 Browder 本质谱的边界性质。第二节证明了比 Snow 得到的更一般的联合Browder 本质谱的谱映象定理。最后在第三节给出了初等算子的 Browder 本质谱表示。

Recently,some excellent achievements in researches of the joint spectrum and thejoint essential spectrum of n-tuple operators have been attained.In this paper,basedon the new achievements mentioned above,the author will discuss the joint Browderessential spectrum of n-tuple operators first defined by Snow and some propertiesabout it.In section 1,the author discusses the boundary prperties of the joint Browderessential spectrum,and in section 2,proves the spectral mapping theorem of the jointBrowder essential spectrum,which is more generalized than the one obtained by Snow.In the last section,the expression of the Browder essential spectrum of elementaryoperators is given.