Drazin invertibility of sum and product of closed linear operators

Bekkai MESSIRDI; Sanaa MESSIRDI; Miloud MESSIRDI

doi:10.26637/mjm204/014

Abstract

The paper present a survey of results concerning the fundamental properties of the Drazin inverse for bounded operators and an interesting study of the Drazin inverse for a closed operator in a Banach space. Some necessary and sufficient conditions for $A$ closed linear operator to possess a Drazin inverse $A^D$ are given, we obtain also a useful caracterization and explicit formula for the Drazin inverse $(A+B)^D$ and $(A B)^D$ if $A$ and $B$ are closed operators.

Keywords:

Drazin inverse, Closed linear operators, Gap metric

Mathematics Subject Classification:

47A05, 47B33

Authors Imprint References Funding Related Articles Downloads

Bekkai MESSIRDI Département de Mathématiques, Université d’Oran (Es-sénia), B.P 1524, El Menouar, Oran. Oran 31000, Algeria.
Sanaa MESSIRDI Département de Mathématiques, Université de Tlemcen . Tlemcen 13000, Algeria.
Miloud MESSIRDI Département de Mathématiques, Université de Tlemcen . Tlemcen 13000, Algeria.

Pages: 472-481
Date Published: 01-10-2014
Vol. 2 No. 04 (2014): Malaya Journal of Matematik (MJM)

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