IJPAM: Volume 22, No. 2 (2005)

WEAKLY g-INVERTIBLE OPERATORS IN
BANACH SPACES AND THEIR
MOORE-PENROSE INVERSE

S. Lahrech$^1$, A. Ouahab$^2$, A. Benbrik$^3$, A. Mbarki$^4$
$^{1,2,3,4}$Department of Mathematics
Faculty of Science
Mohamed First University
Oujda, MOROCCO
$^1$e-mail: lahrech@sciences.univ-oujda.ac.ma
$^2$e-mail: ouahab@sciences.univ-oujda.ac.ma
$^3$e-mail: benbrik@sciences.univ-oujda.ac.ma
$^4$e-mail: mbarki@sciences.univ-oujda.ac.ma


Abstract.In this paper, we define a new class of linear operators called class of weakly g-invertible operators which contains the usual class of g-invertible operators. For such operators, we define their generalized inverse according to a fixed algebrical decomposition. Finally, we prove the existence and the unicity of the Moore-Penrose inverse of weakly g-invertible operators. Our result generalize the result established in [#!r3!#] for g-invertible operators.

Received: June 3, 2005

AMS Subject Classification: 47A53, 47A56

Key Words and Phrases: algebrically decomposable operators, weakly g-invertible operators, generalized inverse of a weakly g-invertible operator, Moore-Penrose inverse, Banach spaces

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 22
Issue: 2