Property(R)for Upper Triangular Operator Matrices  

作　　者：Li Li YANG Xiao Hong CAO 

机构地区：[1]School of Mathematics and Statistics,Shaanxi Normal University,Xi’an 710119,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2023年第3期523-532,共10页数学学报（英文版）

基　　金：Supported by the Fundamental Research Funds for the Central Universities(Grant No.GK 202007002);Nature Science Basic Research Plan in Shaanxi Province of China(Grant No.2021JM-189,2021JM-519)。

摘　　要：Property(R)holds for an operator when the complement in the approximate point spectrum of the Browder essential approximate point spectrum coincides with the isolated points of the spectrum which are eigenvalues of finite multiplicity.Let A∈B(H)and B∈B(K),where H and K are complex infinite dimensional separable Hilbert spaces.We denote by M_(C)the operator acting on H⊕K of the form M_(C)=(AC0B).In this paper,we give a sufficient and necessary condition for M_(C)∈(R)for all C∈B(K,H).

关 键 词：property(R) upper triangular operator matrix SPECTRUM 

分 类 号：O177[理学—数学] O151.21[理学—基础数学]