闭值域稠定闭算子的Moore-Penrose广义逆的有限维逼近

Finite-Dimensional Approximation of the Moore-Penrose Inverse of a Densely Defined Closed Operator with Closed Range

研究了闭值域稠定闭算子的Moore-Penrose广义逆的有限维逼近问题.由于可接受条件相当强,我们提出更弱的条件P_(G(T_n))■P_(G(T))来研究稠定闭算子MoorePenrose广义逆的有限维逼近,也能得到相同的结论.特别地,当T为有界算子且T_n=Q_nTP_n时,条件P_(G(T_n))■P_(G(T))自然成立,于是有界线性算子Moore-Penrose广义逆的有限维逼近的一些结果会成为定理3.3的推论.

We study the problem of finite-dimensional approximation of the Moore- Penrose inverse of a closed densely defined operator with closed range. Because the ad- missible conditions are quite strong, so we put forward the weaker condition PC（Tn） 8→ PG（T） to study finite-dimensional approximation of the Moore-Penrose inverse of a closed densely defined operator, which has the same conclusion. Especially, if T is a bounded linear operator and Tn = QnTPn, then the condition PG（Tn） 8→ PG（T） will hold naturally and many results of the Moore-Penrose inverse of a bounded linear operator be corollaries of Theorem 3.3.