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. https://orcid.org/0000-0002-6625-1393

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).

Biografía del autor

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.

Citas

H. Benbouziane, Y. Bouramdane, M. Ech-Cherif El Kettani, A. Lahssaini: Nonlinear commutant preservers, Linear and Multilinear Algebra 463 No.3, pp. 593-601, (2018).

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

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

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

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).

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).

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

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

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

Publicado
2019-02-26
Cómo citar
[1]
H. Benbouziane, Y. Bouramdane, y M. Ech-Chérif El Kettani, «Nonlinear maps preserving certain subspaces»., PJM, vol. 38, n.º 1, pp. 163-175, feb. 2019.
Sección
Artículos