SciELO - Scientific Electronic Library Online

vol.38 número1Spectra and fine spectra for the upper triangular band matrix U(a 0 , a 1 , a 2 ; b 0 , b 1 , b 2 ) over the sequence space c 0Even vertex equitable even labeling for snake related graphs índice de autoresíndice de materiabúsqueda de artículos
Home Pagelista alfabética de revistas  

Servicios Personalizados




Links relacionados

  • En proceso de indezaciónCitado por Google
  • No hay articulos similaresSimilares en SciELO
  • En proceso de indezaciónSimilares en Google


Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

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


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 :

2 University Sidi Mohamed Ben Abdellah, Faculty of Sciences DharMahraz Fes, Department of Mathematics, 1796 Atlas Fes, Morocco e-mail :

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


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.


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


[1] H. BenbouzianeY. BouramdaneM. Ech-Cherif El Kettani A. Lahssaini : Nonlinear commutant preservers, Linear and Multilinear Algebra 463 No.3, pp. 593-601, (2018). [ Links ]

[2] A. Bourhim, J. Mashreghi and A. Stepanyan, Nonlinear maps preserving the minimum and surjectivity moduli, Linear Algebra Appl. 463, pp. 171-189, (2014). [ Links ]

[3] J. Cui, J. Hou, Additive maps on standard operator algebras preserving invertibilities or zero divisors, Linear Algebra Appl. 359, pp. 219-233, (2003). [ Links ]

[4] J. Cui, J. Hou, Maps leaving functional values of operator products invariant, Linear Algebra Appl.428, pp. 1649-1663, (2008). [ Links ]

[5] G. Doboviek, B. Kuzma, G. Lenjak, C. K. Li, T. Petek, Mappings that preserve pairs of operators with zero triple Jordan product,Linear Algebra Appl. 426, pp. 255-279, (2007). [ Links ]

[6] M. Elhodaibi and A. Jaatit, On Additive maps preserving the hyperrange or hper-kernel of operators, Int. Math. Forum 7 No. 25-28, pp. 1223-1231, (2012). [ Links ]

[7] G. Frobenius, Über die Darstellung der endlichen Gruppen durch lineaire Substitusionen , Sitzungsber Deutsch. Akad. Wiss. Berling(1897),171-172. [ Links ]

[8] M. Oudghiri, Additive mappings preserving the kernel or the range of operators, Extracta Math. 24, pp. 251-258, (2009). [ Links ]

[9] P. Šemrl, Two characterizations of automorphisms on B(X), Studia Math. 150, pp. 143-149, (1993). [ Links ]

Received: April 2018; Accepted: May 2018

Creative Commons License This is an open-access article distributed under the terms of the Creative Commons Attribution License