Symmetry of the Point Spectrum of Upper Triangular Infinite Dimensional Hamiltonian Operators
Received:September 07, 2007  Revised:April 16, 2008
Key Word: non-self-adjoint operator   infinite dimensional Hamiltonian operator   point spectrum   symmetry.
Fund ProjectL: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); Researc
 Author Name Affiliation WANG Hua Department of Mathematics, College of Science and Technology, Inner Mongolia University, Inner Mongolia 010021, China Department of Mathematics, College of Science, Inner Mongolia University of Technology, Inner Mongolia 010051, China Alatancang 内蒙古工业大学理学院数学系, 内蒙古 呼和浩特 010051 HUANG Jun Jie Department of Mathematics, College of Science and Technology, Inner Mongolia University, Inner Mongolia 010021, China
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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 $\sigma_p(A)$ and $\sigma_p^1(-A^*)$ 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.