Spectra Of Some Kinds Of Upper Triangular Operator Matrix

There are three chapters in this thesis, and the main contents are as follow.In chapter 1, the background, advance of completion problems of operator matrices and the main results obtained in the thesis are described.In chapter 2, base on the theory of spectral perturbation, the spectrum of the un-bounded 2×2 upper triangular operator matrices is investigated. It is shown that under some assumptions, their spectrum can be determined by the diagonal elements. Moreover, some examples are presented to illustrate our results.In chapter 3, the intersections of left(right)spectra, the spectra of 3×3 upper trian-gular operator matrices are described.