ACTA MATHEMATICA
UNIVERSITATIS COMENIANAE





Perturbation analysis of bounded homogeneous generalized inverses on Banach spaces

Jianbing Cao and D. Yifeng Xue

Received: February 28, 2013;   Revised: April 2, 2014;   Accepted: May 6, 2014



Abstract.   Let X, Y be Banach spaces and T: X \to Y be a bounded linear operator. In this paper, we initiate the study of the perturbation problems for bounded homogeneous generalized inverse Th and quasi-linear projector generalized inverse Th of T. Some applications to the representations and perturbations of the Moore-Penrose metric generalized inverse TM of T are also given. The obtained results in this paper extend some well-known results for linear operator generalized inverses in this field.

Keywords:  Homogeneous operator; stable perturbation; quasi-additivity; generalized inverse.  

AMS Subject classification: Primary:  47A05   Secondary: 46B20


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Acta Mathematica Universitatis Comenianae
ISSN 0862-9544   (Printed edition)

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