On The Self-adjoint Perturbations Of Spectra Of Upper Triangular Operator Matrices

In 1994,Prof.H.Du et al described the perturbation of the spectrum of upper tri-angular operator matrix.After that,the authors both at home and abroad carried out an intensive research on this topic,and obtained many results with great significance.The Hamiltonian operator has a profound mechanical background,and the perturbations of spectra of this kind of operators are based on the self-adjoint perturbations of spectra of operator matrices.In this thesis,the self-adjoint perturbations of the left spectrum,right spectrum,point spectrum and compression spectrum of upper triangular operator matrix are investigated by means of space decomposition method.Under some conditions,the estimations of the self-adjoint perturbations of the left spectrum,right spectrum,point spectrum and compression spectrum of upper triangular operator matrix are given,when the upper right operator element runs over the set consisting of all bounded self-adjoint operators,and the related results are applied to Hamiltonian operators.