Symmetry of the Point Spectrum of Upper Triangular Infinite Dimensional Hamiltonian Operators  

作　　者：WANG Hua Alatancang HUANG dun die 

机构地区：[1]Department of Mathematics, College of Science and Technology, Inner Mongolia University, Inner Mongolia 010021, China [2]Department of Mathematics, College of Science, Inner Mongolia University of Technology, Inner Mongolia 010051, China

出　　处：《Journal of Mathematical Research and Exposition》2009年第5期907-912,共6页数学研究与评论（英文版）

基　　金：Foundation item： the National Natural Science Foundation of China （No. 10562002）; the Natural Science Foundation of Inner Mongolia （Nos. 200508010103; 200711020106）; the Specialized Research Fund of the Doctoral Program of Higher Education of China （No. 20070126002）; Research Foundation for Talented Scholars of Inner Mongolia University （No. 206029）.

摘　　要：In this paper, by using characterization of the point spectrum of the upper triangular infinite dimensional Hamiltonian operator H, a necessary and sufficient condition is obtained on the symmetry of σP（A） and σ1/P（-A^＊） with respect to the imaginary axis. Then the symmetry of the point spectrum of H is given, and several examples are presented to illustrate the results.In this paper,by using characterization of the point spectrum of the upper triangular infinite dimensional Hamiltonian operator H,a necessary and sufficient condition is obtained on the symmetry of σp(A) and σp1(-A*) with respect to the imaginary axis.Then the symmetry of the point spectrum of H is given,and several examples are presented to illustrate the results.

关 键 词：non-self-adjoint operator infinite dimensional Hamiltonian operator point spectrum symmetry. 

分 类 号：O157.5[理学—数学] O175.1[理学—基础数学]