Abstract
Rank-one perturbations of closed range bounded linear operators on Hilbert space are considered. The Moore–Penrose inverses of these operators are obtained. The results are generalized to obtain the Moore–Penrose inverse of operators of the form \(A+V_{1}GV_{2}^{*}\). Applications to nonnegativity of the Moore–Penrose inverse and operator partial orders are considered.
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Acknowledgements
The first author thanks the Council of Scientific and Industrial Research (CSIR) for financial support in the form of a Senior Research Fellowship.
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Jose, S., Sivakumar, K.C. (2013). Moore–Penrose Inverse of Perturbed Operators on Hilbert Spaces. In: Bapat, R., Kirkland, S., Prasad, K., Puntanen, S. (eds) Combinatorial Matrix Theory and Generalized Inverses of Matrices. Springer, India. https://doi.org/10.1007/978-81-322-1053-5_10
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DOI: https://doi.org/10.1007/978-81-322-1053-5_10
Publisher Name: Springer, India
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