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Representations for Moore-Penrose inverses in Hilbert spaces. (English) Zbl 0982.47003
Let $$H_1$$, $$H_2$$ be Hilbert spaces and let $$T: H_1\to H_2$$ be a bounded linear operator with the closed range. There are given some representations of the perturbation for Moore-Penrose inverse in the case when this perturbation preserves invariant the range or the null space of the operator $$T$$ under consideration.

MSC:
 47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
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References:
 [1] Ben-Israel, A.; Greville, T.N.E., Generalized inverses, theory and applications, (1974), Wiley New York · Zbl 0305.15001 [2] Nashed, M.Z., Generalized inverses and applications, (1976), Academic New York · Zbl 0346.15001 [3] Ding, J.; Huang, L., On the perturbation of the least squares solutions in Hilbert spaces, Linear algb. appl., 212/213, 487-500, (1994) · Zbl 0817.47017 [4] Ben-Israel, A., On error bounds for generalized inverse, SIAM J. numer. anal., 3, 585-592, (1966) · Zbl 0147.13201 [5] Chen, G.; Wei, M.; Xue, Y., Perturbation analysis of the least squares solution in Hilbert spaces, Linear algb. appl., 244, 69-80, (1996) · Zbl 0863.47011 [6] Kato, T., Perturbation theory for linear operators, (1980), Springer-Verlag New York [7] Stewart, G.W., On the continuity of the generalized inverse, SIAM J. appl. math., 17, 33-45, (1969) · Zbl 0172.03801 [8] Stewart, G.W.; Sun, J.-G., Matrix perturbation theory, (1990), Academic Press New York [9] Wedin, P.-A., Perturbation theory for pseudo-inverses, Bit, 13, 217-232, (1973) · Zbl 0263.65047 [10] Wei, Y., Solving singular linear systems and generalized inverse, Ph.D. thesis, (1997), Institute of Mathematics, Fudan University Shanghai, China
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