On the perturbation of the group generalized inverse for a class of bounded operators in Banach spaces |
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Authors: | N Castro-González JY Vélez-Cerrada |
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Institution: | Departamento de Matemática Aplicada, Facultad de Informática, Universidad Politécnica de Madrid, 28660 Boadilla del Monte, Madrid, Spain |
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Abstract: | Given a bounded operator A on a Banach space X with Drazin inverse AD and index r, we study the class of group invertible bounded operators B such that I+AD(B−A) is invertible and R(B)∩N(Ar)={0}. We show that they can be written with respect to the decomposition X=R(Ar)⊕N(Ar) as a matrix operator, , where B1 and are invertible. Several characterizations of the perturbed operators are established, extending matrix results. We analyze the perturbation of the Drazin inverse and we provide explicit upper bounds of ‖B?−AD‖ and ‖BB?−ADA‖. We obtain a result on the continuity of the group inverse for operators on Banach spaces. |
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Keywords: | Drazin inverse Group inverse Bounded operators Matrix operators Resolvent Perturbation |
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