2×2上三角算子矩阵的Drazin谱

Drazin Spectra of 2×2 Upper-triangular Operator Matrices

设■是从Hilbert空间H⊕K到H⊕K中的2×2上三角算子矩阵.该文主要研究M_C的Drazin可逆性和M_C的Drazin谱.此外,对给定算子A∈B(H)和B∈B(K),将给出在一定条件下所有上三角算子矩阵M_C的Drazin谱的交■σ_D(M_C)的具体表达式.

Let Me =[O B ^A C] be a 2 x 2 upper-triangular operator matrix acting on the Hilbert space H ＋ K. In this paper, the authors investigate the Drazin invertibility of Mc and the Drazin spectrum of Mc. Moreover, for given operaters A ∈ B（H） and B ∈ B（K）, they shall give a representation of ∩C∈B（K,H）σD（Mc） under certain condition.