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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.35 no.3 Antofagasta Sept. 2016

http://dx.doi.org/10.4067/S0716-09172016000300007 

 

Non-linear maps preserving singular algebraic operators

 

Mourad Oudghiri

Uiversité Mohammed Premier - Oujda, Maroc

 

Khalid Souilah

Uiversité Mohammed Premier - Oujda, Maroc


ABSTRACT

Let B(H) be the algebra of all bounded linear operators on an infinite-dimensional Hilbert space H. We prove that if Φ is a surjective map on B(H) such that Φ(I) = I + Φ(0) and for every pair T, S ∈ B(H), the operator T — S is singular algebraic if and only if Φ(T) — Φ(S) is singular algebraic, then Φ is either of the form Φ(T) = ATA-1 + Φ(0) or the form Φ(T) = AT*A-1 + Φ(0) where A : H → H is an invertible bounded linear, or conjugate linear, operator.

Subjclass [2000] : 47B49, 47L99, 47A55, 47B37.

Keywords : Non-linear preserver problems, Algebraic operators.


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 Received : March 2016. Accepted : June 2016

 

Mourad Oudghiri
Département Math-Info,
Labo LAGA,
Faculté des Sciences d’Oujda,
Université Mohammed Premier - Oujda, 60000 Oujda,
Maroc
e-mail : morad.oudghiri@gmail.com

Khalid Souilah
Departement Math-Info,
Labo LAGA,
Faculte des Sciences d’Oujda,
60000 Oujda,
Maroc
e-mail : s.khalide@gmail.com

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