Non-linear maps preserving singular algebraic operators

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 &a...

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Autores principales:	Oudghiri,Mourad, Souilah,Khalid
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2016
Materias:	Non-linear preserver problems Algebraic operators.
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172016000300007
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spelling	oai:scielo:S0716-091720160003000072016-10-03Non-linear maps preserving singular algebraic operatorsOudghiri,MouradSouilah,Khalid Non-linear preserver problems Algebraic operators. 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.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.35 n.3 20162016-09-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172016000300007en10.4067/S0716-09172016000300007
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Non-linear preserver problems Algebraic operators.
spellingShingle	Non-linear preserver problems Algebraic operators. Oudghiri,Mourad Souilah,Khalid Non-linear maps preserving singular algebraic operators
description	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.
author	Oudghiri,Mourad Souilah,Khalid
author_facet	Oudghiri,Mourad Souilah,Khalid
author_sort	Oudghiri,Mourad
title	Non-linear maps preserving singular algebraic operators
title_short	Non-linear maps preserving singular algebraic operators
title_full	Non-linear maps preserving singular algebraic operators
title_fullStr	Non-linear maps preserving singular algebraic operators
title_full_unstemmed	Non-linear maps preserving singular algebraic operators
title_sort	non-linear maps preserving singular algebraic operators
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2016
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172016000300007
work_keys_str_mv	AT oudghirimourad nonlinearmapspreservingsingularalgebraicoperators AT souilahkhalid nonlinearmapspreservingsingularalgebraicoperators
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Non-linear maps preserving singular algebraic operators

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