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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.38 no.1 Antofagasta mar. 2019

http://dx.doi.org/10.4067/S0716-09172019000100163 

Articles

Nonlinear maps preserving certain subspaces

H. Benbouziane1 

Y. Bouramdane2 

M. Ech-Chérif El Kettani3 

1 University Sidi Mohamed Ben Abdellah, National School of Applied Sciences, Departement of Industrial Engineering, 1796 Atlas Fes, Morocco e-mail : benbhassan@yahoo.fr

2 University Sidi Mohamed Ben Abdellah, Faculty of Sciences DharMahraz Fes, Department of Mathematics, 1796 Atlas Fes, Morocco e-mail : youssef.bouramdane1@usmba.ac.ma

3 University Sidi Mohamed Ben Abdellah, Faculty of Sciences DharMahraz Fes, Department of Mathematics, 1796 Atlas Fes, Morocco e-mail : melkettani@yahoo.fr

Abstract

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

Texto completo disponible sólo en PDF.

Full text available only in PDF format.

Acknowledgements.

The authors would to thank warmly the anonymous referee for carefully reading the paper and for valuable suggestions

References

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Received: April 2018; Accepted: May 2018

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