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PG(Tn)PG(T)来研究稠定闭算子Moore-Penrose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Tn=QnTPn时,条件PG(Tn)PG(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 admissible conditions are quite strong, so we put forward the weaker condition PG(Tn)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)PG(T) will hold naturally and many results of the Moore-Penrose inverse of a bounded linear operator be corollaries of Theorem 3.3.
稠定闭算子 / 有限维逼近 / Moore-Penrose广义逆 / 图逼近 / 正交投影 {{custom_keyword}} /
closed densely defined operator / finite-dimensional approximation / Moore-Penrose inverse / graph approximation / orthogonal projection {{custom_keyword}} /
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