Hamilton算子的一类n次数值域的对称性

Symmetry of a Class of N-numerical Range for Hamiltonian Operator

以Hamilton算子的数值域为基础,研究了一类算子的二次数值域关于实轴,虚轴的对称性.此外从α-J-自伴算子的n次数值域关于过原点直线对称出发,得到了有界Hamilton算子的一类n次数值域关于虚轴的对称性.

Based on the numerical range of Hamiltonian operator,the symmetry of the real axis and imaginary axis for quadratic numerical range of a class of operator is studied in this article.Furthermore,according to the symmetry of a line through origin for the n-numerical range of α-J-self-adjoint operator,we obtain that a class of n-numerical range for bounded Hamiltonian operator is symmetrical about imaginary axis.