Spectral Properties Of Upper Triangular Operator Matrices

Firstly,the research background of the spectral problem of operator matrices is in-troduced in this thesis.Based on the space decomposition technique,we investigate the spectral property of the upper triangular operator matrix(AOCB)defined on H1(?)H2,where H1 and H2 are infinite-dimensional separable Hilbert spaces.When C? B(H2,H1)is unknown,some sufficient and necessary conditions are given for the residual spectrum.continuous spectrum,Moore-Penrose spectrum,Weyl spectrum,Browder spectrum and Drazin spectrum of the whole operator matrix to be contained in the union of the cor-responding spectra of its diagonal entries.Besides,when C E B(H2,H1)is given,the corresponding problems are considered for upper triangular operator matrices.