Abstract
We investigate the perturbation of the Drazin inverse of a closed linear operator recently introduced by second author and Tran, and derive explicit bounds for the perturbations under certain restrictions on the perturbing operators. We give applications to the solution of perturbed linear equations, to the asymptotic behaviour ofC 0-semigroups of linear operators, and to perturbed differential equations. As a special case of our results we recover recent perturbation theorems of Wei and Wang.
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References
S. L. Campbell, Continuity of the Drazin inverse,Linear and Multilinear Algebra 8 (1980), 265–268.
S. L. Campbell and C. D. Meyer, Continuity properties of the Drazin pseudoinverse,Linear Algebra Appl. 10 (1975), 77–83.
M. P. Drazin, Pseudo-inverse in associative rings and semigroups,Amer. Math. Monthly 65 (1958), 506–514.
J. J. Koliha, A generalized Drazin inverse,Glasgow Math. J. 38 (1996), 367–381.
J. J. Koliha, Isolated spectral points,Proc. Amer. Math. Soc. 124 (1996), 3417–3424.
J. J. Koliha and P. W. Poon, Spectral sets II,Rend. Circ. Mat. (Palermo) 47 (1998), 293–310.
J. J. Koliha and V. Rakoĉević, Continuity of the Drazin inverse II,Studia Math. 131 (1998), 167–177.
J. J. Koliha and T. D. Tran, The Drazin inverse for closed linear operators, preprint.
M. Mbekhta, Généralisation de la décomposition de Kato aux opérateurs paranormaux et spectraux,Glasgow Math. J. 29 (1987), 159–175.
J. van Neerven,The Asymptotic Behaviour of Semigroups of Linear Operators, Birkhäuser, Basel, 1996.
A. Pazy,Semigroups of Linear Operators and Applications to Partial Differential Equation, Springer, New York, 1983.
V. Rakoĉević, Continuity of the Drazin inverse,J. Operator Theory,41 (1999), 55–68.
V. Rakoĉević, and Y. Wei, The perturbation theory for the Drazin inverse and its applications, preprint.
G. Rong, The error bounds for the perturbation of the Drazin inverse,Linear Algebra Appl. 47 (1982), 159–168.
A. E. Taylor and D. C. Lay,Introduction to Functional Analysis, 2nd ed., Wiley, New York, 1980.
Y. Wei and G. Wang, The perturbation theory for the Drazin inverse and its applications,Linear Algebra Appl. 258 (1997), 179–186.