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Representations for the Generalized Inverses of a Modified Operator

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Ukrainian Mathematical Journal Aims and scope

Some explicit representations for the generalized inverses of a modified operator A + Y GZ , where A, Y, Z, and G are operators between Banach spaces, are obtained under certain conditions. The obtained results generalize the recent works on the Drazin inverse and the Moore–Penrose inverse of complex matrices and Hilbert-space operators.

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References

  1. A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications, 2nd ed., Springer, New York (2003).

    MATH  Google Scholar 

  2. J. Chen and Z. Xu, “Representations for the weighted Drazin inverse of a modified matrix,” Appl. Math. and Comput., 203, 202–209 (2008).

    MathSciNet  MATH  Google Scholar 

  3. A. Dajić and J. J. Koliha, “The weighted g-Drazin inverse for operators,” J. Austral. Math. Soc., 82, 163–181 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  4. C. Y. Deng, “A generalization of the Sherman–Morrison–Woodbury formula,” Appl. Math. Lett., 24, 1561–1564 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  5. D. S. Djordjevic and P. S. Stanimirovic, “Splittings of operators and generalized inverses,” Publ. Math. Debrecen., 59, No. 1-2, 147–159 (2001).

    MathSciNet  MATH  Google Scholar 

  6. J. J. Koliha, “A generalized Drazin inverse,” Glasgow Math. J., 38, 367–381 (1996).

    Article  MathSciNet  MATH  Google Scholar 

  7. V. Rakočević, “Moore–Penrose inverse in Banach algebras,” Proc. Roy. Irish Acad. A, 88, 57–60 (1988).

    MathSciNet  Google Scholar 

  8. J. Sherman and W. J. Morrison, “Adjustment of an inverse matrix corresponding to a change in one elements of a given matrix,” Ann. Math. Statist., 21, 124–127 (1950).

    Article  MathSciNet  MATH  Google Scholar 

  9. Y. Wei, “The Drazin inverse of a modified matrix,” Appl. Math. and Comput., 125, 295–301 (2002).

    MathSciNet  MATH  Google Scholar 

  10. M. A. Woodbury, “Inverting modified matrices,” Tech. Rept. Statist. Res. Group, Princeton Univ., Princeton, NJ, 42 (1950).

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Authors and Affiliations

  1. University of Niš, Niš, Serbia

    D. Mosić

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  1. D. Mosić
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, No. 6, pp. 860–864, June, 2016.

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Mosić, D. Representations for the Generalized Inverses of a Modified Operator. Ukr Math J 68, 981–986 (2016). https://doi.org/10.1007/s11253-016-1271-9

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  • DOI: https://doi.org/10.1007/s11253-016-1271-9

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