Pseudospectra Of Infinite-dimensional Hamiltonian Operators

In the thesis,the relation is discussed between the pseudo-point spectrum,the pseudo-residual spectrum and the pseudo-continuous spectrum of the densely defined closed linear op-erators.Moreover,the structure of pseudospectra of infinite-dimensional Hamiltonian operators is given.The first chapter is an introduction that briefly introduces the research background and research status of spectra of infinite-dimensional Hamiltonian operators and pseudospectra of linear operators.In chapter 2,the meticulous classification of the pseudo-point spectrum and pseudo-residual spectrum is given for a densely defined closed linear operator acting on a Hilbert space.And the relations of four types of pseudo-point spectrum and two types of pseudo-residual spectrum are described between linear operator and its adjoint operator.In chapter 3 we study some properties of the pseudo-point spectrum,the pseudo-residual spectrum and the pseudo-continuous spectrum of the densely defined closed linear operators.Furthermore,the structure of pseudospectra of infinite-dimensional Hamiltonian operators is discussed.Finally,the pseudospectra of the upper-triangular Hamiltonian operators are described.