上三角算子矩阵的谱

Spectra of Upper-Triangular Operator Matrices

设X,y是Banach空间,对A∈B(X),B∈B(y),C∈B(Y,X),以M_C记X⊕Y上的算子(ACOB).本文给出了算子M_C的20种谱的结构表示,18种谱的填洞性质以及关于这些问题的有趣例子.

Let X and Y be Banach spaces, A∈ B（X）, B∈ B（Y）, C ∈ B（Y,X）, Mc = （A C O B） be the operator matrix acting on the Banach space X ＋ Y. In this paper, we give out 20 kind spectra structure of Mc, decide 18 kind spectra filling-in-hole properties of Mc and present some interesting examples of these problems.