2*2上三角算子矩阵的Browder定理

Browder's theorem for 2*2 upper triangular operator matrices

设Mc=A C0 B∈B(XY)为定义在Banach空间X Y上的上三角算子矩阵,讨论了Browder定理对Mc成立的一些充分条件,并对文献[9]中的定理2.1举反例指明失误,并进行了修正.

Abstract： Let Mc （A0 CB） ∈ B（X ＋ Y） be an upper triangular operator acting on the Banaeh spaces B （X ＋Y）, this paper explores the condition under which Browder＇s theorem survive for upper triangular operator matrices. And by giving a counter - example, the author points out that one of the result（theorem 2.1 ） in the paper[9] is wrong, and provides a solution.