On the generalized Drazin inverse and generalized resolvent

Dragan S. Djordjević; Stanimirović, Predrag S.

Czechoslovak Mathematical Journal (2001)

  • Volume: 51, Issue: 3, page 617-634
  • ISSN: 0011-4642

Abstract

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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 -algebras is considered. We investigate the generalized Drazin inverse as an outer inverse with prescribed range and kernel. Also, operator matrices are considered. As corollaries, we get some well-known results.

How to cite

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Djordjević, Dragan S., and Stanimirović, Predrag S.. "On the generalized Drazin inverse and generalized resolvent." Czechoslovak Mathematical Journal 51.3 (2001): 617-634. <http://eudml.org/doc/30659>.

@article{Djordjević2001,
abstract = {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, $2\times 2$ operator matrices are considered. As corollaries, we get some well-known results.},
author = {Djordjević, Dragan S., Stanimirović, Predrag S.},
journal = {Czechoslovak Mathematical Journal},
keywords = {Drazin inverse; generalized resolvent; limit processes; outer inverses; operator matrices; Drazin inverse; generalized resolvent; limit processes; outer inverses; operator matrices},
language = {eng},
number = {3},
pages = {617-634},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the generalized Drazin inverse and generalized resolvent},
url = {http://eudml.org/doc/30659},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Djordjević, Dragan S.
AU - Stanimirović, Predrag S.
TI - On the generalized Drazin inverse and generalized resolvent
JO - Czechoslovak Mathematical Journal
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 3
SP - 617
EP - 634
AB - 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, $2\times 2$ operator matrices are considered. As corollaries, we get some well-known results.
LA - eng
KW - Drazin inverse; generalized resolvent; limit processes; outer inverses; operator matrices; Drazin inverse; generalized resolvent; limit processes; outer inverses; operator matrices
UR - http://eudml.org/doc/30659
ER -

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