研究了无穷维Hamilton算子的数值域.首先得到了无穷维Hamilton算子的数值域和谱集之间的关系.其次给出无穷维Hamilton算子的数值域关于虚轴对称的充分条件.最后举例验证了我们结论的正确性.

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.