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Group inverse and generalized Drazin inverse of block matrices in a Banach algebra

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Necessary and sufficient conditions for the existence of the group inverse of an anti-triangular block matrix in Banach algebras are presented. Using these results, we give the formulae for the generalized Drazin inverse of a block matrix.

Abstract

Necessary and sufficient conditions for the existence of the group inverse of an anti-triangular block matrix in Banach algebras are presented. Using these results, we give the formulae for the generalized Drazin inverse of a block matrix.

참고문헌 (10)

  1. C. Bu, "Some results on group inverses of block matrices over skew fields", Electron. J. Linear Algebra, 18, pp.117~125 (2009)
  2. S. L. Campbell, "Generalized Inverses of Linear Transformations" (1979), Pit-man
  3. N. Castro-Gonz´alez, "Representations of the Drazin inverse for a class of block matrices", Linear Algebra Appl, 400, pp.253~269 (2005)
  4. N. Castro-Gonz´alez, "New additive results for the g-Drazin inverse", Proc. Roy. Soc. Edinburgh Sect. A, 134(6), pp.1085~1097 (2004)
  5. C. Cao, "A note on the group inverse of some 2 × 2 block matrices over skew fields", Appl. Math. Comput, 217(24), pp.10271~10277 (2011)
  6. C. Deng, "A note on the Drazin inverse of an anti-triangular matrix", Linear Algebra Appl, 431(10), pp.1910~1922 (2009)
  7. D. S. Djordjevi´c, "Additive results for the generalized Drazin inverse", J. Aust. Math. Soc, 73(1), pp.115~125 (2002)
  8. R. E. Hartwig, "Some additive results on Drazin inverse", Linear Algebra Appl, 322(1-3), pp.207~217 (2001)
  9. J. J. Koliha, "A generalized Drazin inverse", Glasgow Math. J, 38(3), pp.367~381 (1996)
  10. X. Liu, "Further results on the group inverses and Drazin inverses of anti-triangular block matrices", Appl. Math. Comput, 218(17), pp.8978~8986 (2012)

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