On the Origin and Numerical Range of Bounded Operators  

作　　者：Xiao Hong WU Jun Jie HUANG ALATANCANG 

机构地区：[1]School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,P.R.China [2]Department of Mathematics,Hohhot Minzu College,Hohhot 010051,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2019年第10期1715-1722,共8页数学学报（英文版）

基　　金：Supported by the NNSF of China(Grant Nos.11761029,11461049,11371185,11661034 and 11761055);the NSF of Inner Mongolia(Grant No.2017MS0123);the key Science and Technology Program of Colleges and Universities of Inner Mogolia(Grant No.NJZY17234)

摘　　要：Numerical range has an important applications on spectrum distribution of operators. In this paper, we devoted to characterizing operators whose numerical range contains the origin. Some necessary and sufficient conditions are given by operator decomposition technique and constructive methods. Furthermore, the closeness of the numerical range of a given operator is also investigated.Numerical range has an important applications on spectrum distribution of operators. In this paper, we devoted to characterizing operators whose numerical range contains the origin. Some necessary and sufficient conditions are given by operator decomposition technique and constructive methods. Furthermore, the closeness of the numerical range of a given operator is also investigated.

关 键 词：BOUNDED LINEAR OPERATOR NUMERICAL RANGE ORIGIN 

分 类 号：O1[理学—数学]