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The representation and approximations of outer generalized inverses

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Abstract

We present a unified representation theorem for the class of all outer generalized inverses of a bounded linear operator. Using this representation we develop a few specific expressions and computational procedures for the set of outer generalized inverses. The obtained result is a generalization of the well-known representation theorem of the Moore--Penrose inverse as well as a generalization of the well-known results for the Drazin inverse and the generalized inverse AT,S (2). Also, as corollaries we get corresponding results for reflexive generalized inverses.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Niš, P.O. Box 224, Višegradska 33, 18000, Niš, Serbia

    D.S. Djordjević

  2. Department of Mathematics, Faculty of Science, University of Niš Faculty of Philosophy, Department of Mathematics, P.O. Box 224, Višegradska 33, 18000, Niš, Serbia

    P.S. Stanimirović

  3. Department of Mathematics and Laboratory of Mathematics for Nonlinear Science, Fudan University, Shanghai, 200433, P. R. China

    Y. Wei

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  1. D.S. Djordjević
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  2. P.S. Stanimirović
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  3. Y. Wei
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Djordjević, D., Stanimirović, P. & Wei, Y. The representation and approximations of outer generalized inverses. Acta Mathematica Hungarica 104, 1–26 (2004). https://doi.org/10.1023/B:AMHU.0000034359.98588.7b

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  • DOI: https://doi.org/10.1023/B:AMHU.0000034359.98588.7b

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