The Spectral Analysis Of Anti-triangular Operator Matrices

Anti-triangular operator matrix has important application in the field of mathe-matical physics.In this thesis,the location of the essential spectrum,accumulation point of the non-real spectrum and spectral estimation of some anti-triangular operator matrices are studied.Firstly,the essential spectral estimation and the accumulation point of the non-real spectrum of three kinds of anti-triangular operator matrices are investigated.We describe the essential spectrum of operator matrices by using the quadratic operator pencil and the properties of its operator entries,and estimate the essential spectrum of the whole operator matrix by using the essential spectrum of the operator entries of the matrix.Then,by using the properties of(?)-self-adjoint operator matrices,the accumulation point of the non-real spectrum of the operator matrices are analyzed.Secondly,for unbounded operator(?),the location of the essential spectrum and spectral inclusion properties are studied.When A and B are self-adjoint operators,the location of the essential spectrum of the operator matrix(?)is described in the general Hilbert space H × H.When A is a self-adjoint and uniformly positive operator,the essential spectrum of the operator matrix(?)is equivalently estimated in the Hilbert space H1/2 × H,where H1/2=D(A1/2).And the spectrum enclosure of unbounded operators(?)is estimated by using the quadratic numerical range of operator matrix(?)|H1×H1,where(?)|H1×H1=T2.