2×2-上三角算子矩阵谱的Fredholm扰动

Fredholm Perturbation of Spectra of 2×2-Upper Triangular Matrices

设H和K是复无穷维可分Hilbert空间,A∈B(H),B∈B(K),C∈B(K,H)且M_C=(ACOB).本文给出了上三角算子矩阵M_C的Weyl谱、本性谱、谱、左谱、右谱、下半本性谱、下半Weyl谱和上半Weyl谱的Fredholm扰动的完全刻画.

Let H and K be complex infinite dimensional separable Hilbert spaces, A ∈ B（H）, B ∈B（K）, C ∈ B（K, H） and Mc = （A C O B）. In this paper, we characterize completely the Fredholm perturbation for the Weyl spectrum, essential spectrum, spectrum, left spectrum, right spectrum, lower semi-Fredholm spectrum, lower semi-Weyl spectrum and upper semi-Weyl spectrum of the upper triangular operator matrices Mc.