本文研究了自伴算子的构造方法,基此得到一类上三角算子矩阵谱的自伴扰动.结果表明对于此类算子,其谱的自伴扰动包含通常的谱扰动,并举例说明后者可以是前者的真子集.作为应用,将上述结果推广到无穷维Hamilton算子情形.
In this paper,we first investigate method of constructing self-adjoint operators. Then,based on the method,the self-adjoint perturbation of spectra of a class of upper triangular operator matrices is obtained.It can be seen that the self-adjoint perturbation of spectra contains the general perturbation of spectra.Moreover,an interesting example shows that this kind of inclusion may be proper.As an application, these results are developed to infinite dimensional Hamiltonian operators.