Moore-Penrose inverse of linear operators in Hilbert space

[摘要] In this paper, we investigate properties of  with closed range satisfying the operator equations    In particular, we investigate the invertibility of    with closed range where the Moore-Penrose inverse of T turns out to be the usual inverse of T under some classes of operators. We also deduce the Moore-Penrose inverse of a perturbed linear operator  with closed range where  such that  has closed ranges and  satisfying some given conditions. The relation between the ranges and null spaces of these operators is also shown.

[学科分类] 计算机科学（综合）

[关键词] Moore-Penrose inverse;perturbed linear operator;invertibility of operators.