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.

Keywords: Generalized inverses, Jordan homomorphism, linear preserver problems.

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