闭值域稠定闭算子的Moore-Penrose广义逆的有限维逼近

邱仁军

数学学报 ›› 2016, Vol. 59 ›› Issue (6) : 835-846.

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PDF(464 KB)
数学学报 ›› 2016, Vol. 59 ›› Issue (6) : 835-846. DOI: 10.12386/A2016sxxb0074
论文

闭值域稠定闭算子的Moore-Penrose广义逆的有限维逼近

    邱仁军
作者信息 +

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

    Ren Jun QIU
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文章历史 +

摘要

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PGTnPGT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PGTnPGT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.

Abstract

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.

关键词

稠定闭算子 / 有限维逼近 / Moore-Penrose广义逆 / 图逼近 / 正交投影

Key words

closed densely defined operator / finite-dimensional approximation / Moore-Penrose inverse / graph approximation / orthogonal projection

引用本文

导出引用
邱仁军. 闭值域稠定闭算子的Moore-Penrose广义逆的有限维逼近. 数学学报, 2016, 59(6): 835-846 https://doi.org/10.12386/A2016sxxb0074
Ren Jun QIU. Finite-Dimensional Approximation of the Moore-Penrose Inverse of a Densely Defined Closed Operator with Closed Range. Acta Mathematica Sinica, Chinese Series, 2016, 59(6): 835-846 https://doi.org/10.12386/A2016sxxb0074

参考文献

[1] Du N. L., The basic principles for stable approximations to orthogonal generalized inverses of linear operators in Hilbert spaces, Numer. Funct. Anal. Optim., 2005, 26:675-708.
[2] Du N. L., Strong convergence criteria for sequences of orthogonal projections and Galerkin approximations for generalized inverses, Acta Math. Sinica, Chin. Ser., 2007, 50(1):43-54.
[3] Du N. L., Finite-dimensional approximation settings for infinite-dimensional Moore-Penrose inverses, SIAM J. Numer. Anal., 2008, 46:1454-1482.
[4] Groetsch C. W., Katzenstein P. J., Keohane R. O., Stable Approximate Evaluation of Unbounded Operators, Springer, New York, 2007.
[5] Groetsch C. W., Generalized Inverses of Linear Operators:Representation and Approximation, Dekker, New York, 1977.
[6] Huang Q., Zhai W., Perturbations and expressions for generalized inverses in Banach spaces and MoorePen-rose inverses in Hilbert spaces of closed linear operators, Linear Algebra Appl., 2011, 435(1):117-127.
[7] Izumino S., Convergence of generalized inverses and spline projectors, J. Approx. Theory, 1983, 38:269-278.
[8] Kulkarni S. H., Nair M. T., Ramesh G., Some properties of unbounded operators with closed range, Proc. Math. Sci., 2008, 118(4):613-625.
[9] Kulkarni S. H., Ramesh G., Projection methods for computing Moore-Penrose inverses of unbounded oper-ators, Indian J. Pure and Appl. Math., 2010, 41(5):647-662.
[10] Kulkarni S. H., Ramesh G., The carrier graph topology, Banach J. Math. Anal., 2011, 5(1):56-69.
[11] Kato T., Perturbation Theory for Linear Operators, Springer-Verlag, New York, 1984.
[12] Locker J., Functional Analysis and Two-point Differential Operators, Longman Scientific Technical, New York, 1986.
[13] Nashed M. Z., Votruba G. F., Generalized Inverses and Applications, Academic Press, New York, 1976:1-109.
[14] Stewart G. W., On the perturbation of pseudo-inverse, projections and linear least squares problems, SIAM Review, 1977, 19:634-662.
[15] Wang Y., Zhang H., Perturbation analysis for oblique projection generalized inverses of closed linear operators in Banach spaces, Linear Algebra Appl., 2007, 426(1):1-11.
[16] Xue Y., Chen G., Some equivalent conditions of stable perturbation of operators in Hilbert spaces, App. Math. Comput., 2004, 147:765-772.
[17] Xue Y., Stable Perturbations of Operators and Related Topics, World Scientific, Singapore, 2012.

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