Banach空间上算子矩阵外逆的表示

The expression for outer inverse of operator matrix on Banach space

设X,Y为Banach空间,B(X,Y)为X到Y的有界线性算子全体,A,B,C,D∈B(X,Y),U,V分别为空间X⊕X,Y⊕Y的子空间.借助于外逆的扰动,得到算子矩阵R=(A B C D)∈B(X⊕X,Y⊕Y)的外逆R(2)U,V的表示.

Let X,Ybe Banach spaces.B（X,Y） denotes the set of all bounded linear operators fromXto Yand A,B,C,D∈B（X,Y）.U,Vare subspaces of X⊕X,Y⊕Y,respectively.In virtue of the perturbation of outer inverse,the expression of outer inverse R（2） U,V of operator matrix R= （A B C D） ∈B（X⊕X,Y⊕Y） is obtained in this paper.