Nonlinear maps preserving certain subspaces.

• Benbouziane, H. ^[1] ; Bouramdane, Y. ^[1] ; Ech-Chérif El Kettani, M. ^[1]
  1. [1] Sidi Mohamed Ben Abdellah University

     Sidi Mohamed Ben Abdellah University

     Fes-Medina, Marruecos

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 38, Nº. 1, 2019, págs. 163-175
• Idioma: inglés
• DOI: 10.4067/s0716-09172019000100163
• Enlaces
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• Resumen

  • 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).

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