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Let H and K be Hilbert spaces and let T,T = T+δTbe bounded operators from H into K. In this article, two facts related to the perturbation bounds are studied. The first one is to find the upper bound of ∥T+T − T+T∥, which extends the results obtained by the second author and enriches the perturbation theory for the Moore-Penrose inverse. The other one is to develop explicit representations of projectors ∥T+T − T+T∥and ∥T+T − T+T∥. In addition, some spectral cases related to these results are analyzed.
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참고문헌 (21)
참고문헌 신청
C. W. Groetsch / 1977 / Generalized Inverses of Linear Operators: representation and approximation, Monographs and Textbooks in Pure and Applied Mathematics, No. 37 / Marcel Dekker, Inc
C. Zhu / 2003 / Perturbation analysis for the reduced minimum modulus of bounded linear operator in Banach spaces / Appl. Math. Comput. 145 (1) : 13 ~ 21
G. Chen / 1996 / Perturbation analysis of the least squares solution in Hilbert spaces / Linear Algebra Appl. 244 : 69 ~ 80
G. Chen / 1997 / Perturbation analysis for the operator equation Tx = b in Banach spaces / J. Math. Anal. Appl. 212 (1) : 107 ~ 125
G. Chen / 1998 / The expression of the generalized inverse of the perturbed operator under Type I perturbation in Hilbert spaces / Linear Algebra Appl. 285 (1) : 1 ~ 6
C. Zhu / 2003 / Perturbation analysis for the reduced minimum modulus of bounded linear operator in Banach spaces / Appl. Math. Comput. 145 (1) : 13 ~ 21
G. Chen / 1996 / Perturbation analysis of the least squares solution in Hilbert spaces / Linear Algebra Appl. 244 : 69 ~ 80
G. Chen / 1997 / Perturbation analysis for the operator equation Tx = b in Banach spaces / J. Math. Anal. Appl. 212 (1) : 107 ~ 125
G. Chen / 1998 / The expression of the generalized inverse of the perturbed operator under Type I perturbation in Hilbert spaces / Linear Algebra Appl. 285 (1) : 1 ~ 6
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