On the Generalized Drazin Inverse and Generalized Resolvent

被引：0
作者：
Dragan S. Djordjevic
Predrag S. Stanimirovic
机构：
[1] University of Nis,Faculty of Sciences, Department of Mathematics
来源：
Czechoslovak Mathematical Journal | 2001年 / 51卷
关键词：
Drazin inverse; generalized resolvent; limit processes; outer inverses; operator matrices;
D O I：
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学科分类号：
摘要：
We investigate the generalized Drazin inverse and the generalized resolvent in Banach algebras. The Laurent expansion of the generalized resolvent in Banach algebras is introduced. The Drazin index of a Banach algebra element is characterized in terms of the existence of a particularly chosen limit process. As an application, the computing of the Moore-Penrose inverse in >C*-algebras is considered. We investigate the generalized Drazin inverse as an outer inverse with prescribed range and kernel. Also, 2 × 2 operator matrices are considered. As corollaries, we get some well-known results.
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页码：617 / 634
页数：17
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共 27 条
  • [1] Ben-Israel A.(1969)On matrices of index zero or one SIAM J. Appl. Math. 17 1118-1121
  • [2] Campbell S. L.(1976)Applications of the Drazin inverse to linear systems of differential equations with singular constant coefficients SIAM J. Appl. Math. 31 411-425
  • [3] Meyer C. D.(1998)Transfer functions and spectral projections Publ. Math. Debrecen 52 367-376
  • [4] Rose N. J.(1975)Representation of the generalized inverse J. Math. Anal. Appl. 49 154-157
  • [5] Förster K.-H.(1990)An imbedding method for computing the generalized inverse J. Comput. Math. 8 353-362
  • [6] Nagy B.(1995)Limiting expression for generalized inverse Numerical Mathematics 4 25-30
  • [7] Groetch C.W.(1984), Irish Math. Soc. Newsletter 11 10-15
  • [8] Guorong W.(1991) and its corresponding projectors Panamer. Math. J. 1 10-16
  • [9] Guorong W.(1992)Spectral projections Studia Math. 103 71-77
  • [10] Wei Y.(1994)On quasinilpotents in rings Appl. Math. Comput. 61 151-156
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