Nonlinear maps preserving certain subspaces.


  • H. Benbouziane University Sidi Mohamed Ben Abdellah.
  • Y. Bouramdane University Sidi Mohamed Ben Abdellah.
  • M. Ech-Chérif El Kettani University Sidi Mohamed Ben Abdellah.


Kernel operator, Nonlinear preservers problem, Range operator


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).

Author Biographies

H. Benbouziane, University Sidi Mohamed Ben Abdellah.

National School of Applied Sciences, Departement of Industrial Engineering.

Y. Bouramdane, University Sidi Mohamed Ben Abdellah.

Faculty of Sciences DharMahraz Fes, Department of Mathematics.

M. Ech-Chérif El Kettani, University Sidi Mohamed Ben Abdellah.

Faculty of Sciences DharMahraz Fes, Department of Mathematics.


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How to Cite

H. Benbouziane, Y. Bouramdane, and M. Ech-Chérif El Kettani, “Nonlinear maps preserving certain subspaces.”, Proyecciones (Antofagasta, On line), vol. 38, no. 1, pp. 163-175, Feb. 2019.




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