Moore–Penrose Inverse of Perturbed Operators on Hilbert Spaces

Shani Jose () and K. C. Sivakumar ()
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Shani Jose: Indian Institute of Technology Madras, Department of Mathematics
K. C. Sivakumar: Indian Institute of Technology Madras, Department of Mathematics

A chapter in Combinatorial Matrix Theory and Generalized Inverses of Matrices, 2013, pp 119-131 from Springer

Abstract: 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.

Keywords: Moore–Penrose inverse; Bounded linear operator; Rank-one perturbation; Partial order; 15A09; 47A55 (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-81-322-1053-5_10

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DOI: 10.1007/978-81-322-1053-5_10

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