Abstract

BENBOUZIANE, H.; BOURAMDANE, Y.  and  KETTANI, M. Ech-Chérif El. Nonlinear maps preserving certain subspaces. Proyecciones (Antofagasta) [online]. 2019, vol.38, n.1, pp.163-175. ISSN 0716-0917.  http://dx.doi.org/10.4067/S0716-09172019000100163.

Let X be a Banach space and let B(X) be the Banach algebra of all bounded linear operators on X. We characterise surjective (not necessarily linear or additive) maps ϕ : B(X) → B(X) such that F(ϕ (A)◇ ϕ (B)) = F(A ◇ B) for all A,B ∈ B(X) where F(A) denotes any of R(A) or N(A), anda ◇ B denotes any binary operations A−B, AB and ABA for all A,B ∈B(X).

Keywords : Kernel operator; Nonlinear preservers problema; Range operator.

        · text in English     · English ( pdf )