Study On The Spectra Of Operator Matrices

This thesis studies on a few topics of the spectra of operator matrices, which being hotly discussed recently, and gets some innovative results. Chapter 3 is the main part of this work, focusing on the filling holes problems of various special operator spectra on Banach spaces. Firstly, it extends the series results on Hilbert spaces to Banach spaces including seven cases such as σ_w, σ_l, σ_le, σ_re, σ_e,σ_lb,σ_k2. Then, it discusses the following six cases on Banach spaces: σ_r, σ_lw, σ_rw, σ(rb), σ_b, σ_k1, which are new and even not having been discussed on Hilbert spaces. Chapter 4 is about some results of Weyl's theorem and Browder's theorem.