一类无穷维Hamilton算子的谱刻画及其可逆性  

SPECTRUM AND INVERTIBILITY OF A CLASS OF INFINITE DIMENSIONAL HAMILTONIAN OPERATORS

作　　者：范小英 阿拉坦仓[2] 

机构地区：[1]北京第12中学,北京100071 [2]内蒙古大学理工学院数学系,呼和浩特010021

出　　处：《系统科学与数学》2011年第1期57-64,共8页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(10562002);内蒙古自治区自然科学基金(200508010103)资助项目

摘　　要：研究了定义域为对角形的上三角无穷维Hamilton算子:H=的谱刻画及其可逆性;当A的剩余谱不含关于虚轴对称的点时,H的谱等于A的谱与A的谱关于虚轴对称分支的并集,并得到了H的预解集为空及其可逆的充要条件;作为结论的应用,得到当A为无穷维Hamilton算子时,H的点谱、剩余谱、连续谱和谱分别等于A的点谱、剩余谱、连续谱和谱.This paper is concerned with the spectrum and invertibility of a class of infinite dimensional Hamiltonian operators described by H =[],where D（H）= D（A）×D（—A~＊） and A is a linear operator in a Hilbert space.If residual spectrum of A excludes the symmetric point about imaginary axis,then the spectrum of H is composed of the spectrum of A and its symmetric points about imaginary axis.The sufficient and necessary conditions for the resolvent set of H to be empty and for H to be invertible are obtained. In particular,if A itself is a Hamiltonian operator,the point spectrum,residual spectrum, continuous spectrum of H is exactly same as those of A.

关 键 词：算子矩阵 无穷维 HAMILTON算子 谱 

分 类 号：O177[理学—数学]