TY - JOUR AU - Benbouziane, H. AU - Bouramdane, Y. AU - Ech-Chérif El Kettani, M. PY - 2019/02/26 Y2 - 2024/03/28 TI - Nonlinear maps preserving certain subspaces. JF - Proyecciones (Antofagasta, On line) JA - Proyecciones (Antofagasta, On line) VL - 38 IS - 1 SE - DO - UR - https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/3417 SP - 163-175 AB - 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). ER -