Journal of Operator Theory

Volume 64, Issue 1, Summer 2010 pp. 117-130.

Additive maps preserving strongly generalized inverses

Authors: Nadia Boudi (1) and Mostafa Mbekhta (2)
Author institution: (1) Departement de Mathematiques, Faculte des Sciences, Universite My Ismail, Meknes, Maroc
(2) UFR de Mathematiques, Universite Lille I, 59655 Villeneuve d'Ascq Cedex, France

Summary: Let

$\A, \B$ be unital complex Banach algebras. An additive map

$\phi$ from

$\A$ to

$\B$ is said to preserve strongly generalized inverses if

$\phi(a)$ is a generalized inverse of

$\phi (b)$ whenever

$a$ is a generalized inverse of

$b$ . In this paper, we characterize additive maps preserving strongly generalized inverses.

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