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/...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.展开更多
基金Foundation item： the National Natural Science Foundation of China （No. 10562002） the Natural Science Foundation of Inner Mongolia （Nos. 200508010103+2 种基金 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）.
文摘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.
