Acta mathematica scientia,Series B ›› 2015, Vol. 35 ›› Issue (6): 1483-1491.doi: 10.1016/S0252-9602(15)30069-2

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A NOTE ON THE REPRESENTATIONS FOR THE GENERALIZED DRAZIN INVERSE OF BLOCK MATRICES

Dijana MOSIC   

  1. Faculty of Sciences and Mathematics, University of Niš, P.O. Box 224, 18000 Niš, Serbia
  • Received:2014-11-28 Revised:2014-06-02 Online:2015-11-01 Published:2015-11-01
  • Supported by:

    The work was supported by the Ministry of Education and Science, Republic of Serbia (174007).

Abstract:

We present some representations for the generalized Drazin inverse of a block matrix x= in a Banach algebra A in terms of ad and (bc)d under certain conditions, extending some recent result related to the generalized Drazin inverse of an anti-triangular operator matrix. Also, several particular cases of this result are considered.

Key words: generalized Drazin inverse, block matrix, Banach algebra

CLC Number: 

  • 46H05
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