Invertible completions of 2 x 2 upper triangular operator matrices

被引：181

作者：

Han, JK ^{[1
]}

Lee, HY

Lee, WY

机构：

[1] Mokwon Univ, Dept Math Educ, Daejon 301719, South Korea

[2] Woosuk Univ, Dept Math, Wanju Gun, Cheonbuk, South Korea

[3] Sung Kyun Kwan Univ, Dept Math, Suwon 440746, South Korea

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2000年 / 128卷 / 01期

关键词：

spectrum; regular; 2 x 2 upper triangular operator matrices;

D O I：

10.1090/S0002-9939-99-04965-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note we prove that if [GRAPHICS] is a 2 x 2 upper triangular operator matrix acting on the Banach space X + Y, then M-C is invertible for some C is an element of L (Y, X) if and only if A is an element of L (X) and B is an element of L (Y) satisfy the following conditions: (i) A is left invertible; (ii) B is right invertible; (iii) X/A(X) congruent to B-1 (0). Furthermore we show that sigma(A) boolean OR sigma(B) = (M-C) boolean OR W, where W is the union of certain of the holes in sigma(M-C) which happen to be subsets of sigma(A) boolean AND sigma(B).

引用

页码：119 / 123

页数：5