In this paper, the numerical range of infinite dimensional Hamiltonian operator is studied. Firstly a relationship between the spectrum and the numerical range for infinite dimensional Hamiltonian operator is considered. Then, a sufficient condition is obtained for the numerical range of infinite dimensional Hamiltonian perator to be symmetric with respect to imaginary axis. Finally, an example is given to illustrate the crrectness of our results.
Alatancang, HAI Guojun, WU Deyu.
NUMERICAL RANGE OF INFINITE DIMENSIONAL HAMILTONIAN OPERATOR. Journal of Systems Science and Mathematical Sciences, 2013, 33(4): 506-510 https://doi.org/10.12341/jssms12080