The Spectra And Invertibility Of Skew-Hamiltonian Operators

In this thesis,we mainly study the spectra and the invertibility of the infinite dimen-sional skew-Hoaniltonian operators,and give the complete characterization of the spectra and the necessary and sufficient condition m the invertibility of the infinite dimensional skew-Hamiltonian operators.In the invertibility,we mainly discuss the invertibility of the infinite dimensional skew-Hamiltonian operators.According to the special structure of the operator itself,we obtain a necessary and sufficient condition:the infinite dimensional skew-Hamiltonian operator has bounded inverse if and only if it has lower boundness.At the same time, we give some examples to illustra.te this.In the spectrum,we discuss the point spectrum, residual spectrum,continuous spectrum and resolvent set of the diagonal,triangular of infinite dimensional skew-Hamiltonian operators,and find that the characterization of the symmetry with respect to the real axis of point spectrum and continuous spectrum, continuous spectrum and resolvent set,and give the necessary and sufficient condition that the residual spectrum of infinite dimensional skew-Hamiltonian operators is empty; Secondly,we research the relations of the spectra between the infinite dimensional skewHamiltonian operator and its conjugate operator:corresponding spectrum are the same; Finally,specific examples are given to illustrate the effectiveness of the above conclusions.