African Journal of
Mathematics and Computer Science Research

  • Abbreviation: Afr. J. Math. Comput. Sci. Res.
  • Language: English
  • ISSN: 2006-9731
  • DOI: 10.5897/AJMCSR
  • Start Year: 2008
  • Published Articles: 256

Full Length Research Paper

Moore-Penrose inverse of linear operators in Hilbert space

J. M. Mwanzia
  • J. M. Mwanzia
  • Department of Mathematics and Actuarial Science, Kenyatta University, P. O. Box 43844 - 00100 Nairobi, Kenya.
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M. Kavila
  • M. Kavila
  • Department of Mathematics and Actuarial Science, Kenyatta University, P. O. Box 43844 - 00100 Nairobi, Kenya.
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J. M. Khalagai
  • J. M. Khalagai
  • School of Mathematics, University of Nairobi, P. O. Box 30197- 00100 Nairobi, Kenya.
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  •  Received: 18 July 2022
  •  Accepted: 25 October 2022
  •  Published: 30 November 2022

Abstract

In this paper, we investigate properties of  with closed range satisfying the operator equations   In particular, we investigate the invertibility of   with closed range where the Moore-Penrose inverse of T turns out to be the usual inverse of T under some classes of operators. We also deduce the Moore-Penrose inverse of a perturbed linear operator  with closed range where  such that  has closed ranges and  satisfying some given conditions. The relation between the ranges and null spaces of these operators is also shown.

Key words: Moore-Penrose inverse, perturbed linear operator, invertibility of operators.