Maps preserving fixed points of generalized product of operators

Abstract Let B(X) be the algebra of all bounded linear operators in a complex Banach space X. For A ∈ B(X) let F (A) be the subspace of fixed point of A. For an integer k ≥ 2, let (i 1 , .., i m ) be a finite sequence with terms chosen from {1, · · · , k}, and assume at least o...

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Autores principales:	Bouramdane,Y., Ech-Cherif El Kettani,M., Elhiri,A., Lahssaini,A.
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2020
Materias:	Fixed point Generalized product Preserver problems
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000501157
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spelling	oai:scielo:S0716-091720200005011572020-11-16Maps preserving fixed points of generalized product of operatorsBouramdane,Y.Ech-Cherif El Kettani,M.Elhiri,A.Lahssaini,A. Fixed point Generalized product Preserver problems Abstract Let B(X) be the algebra of all bounded linear operators in a complex Banach space X. For A ∈ B(X) let F (A) be the subspace of fixed point of A. For an integer k ≥ 2, let (i 1 , .., i m ) be a finite sequence with terms chosen from {1, · · · , k}, and assume at least one of the terms in (i 1 , · · · , i m ) appears exactly once. The generalized product of k operators A 1 , ..., A k ∈ B(X) is defined by A 1 ∗ A 2 ∗ · · · ∗ A k = A i ₁ A i ₂ · · · A i m , and includes the usual product and the triple product. We characterize the form of maps from B(X) onto itself satisfying F (ϕ(A 1 ) ∗ · · · ∗ ϕ(A k )) = F (A 1 ∗ · · · ∗ A k ) for all A 1 , · · · , A k ∈ B(X).info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.39 n.5 20202020-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000501157en10.22199/issn.0717-6279-2020-05-0071
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Fixed point Generalized product Preserver problems
spellingShingle	Fixed point Generalized product Preserver problems Bouramdane,Y. Ech-Cherif El Kettani,M. Elhiri,A. Lahssaini,A. Maps preserving fixed points of generalized product of operators
description	Abstract Let B(X) be the algebra of all bounded linear operators in a complex Banach space X. For A ∈ B(X) let F (A) be the subspace of fixed point of A. For an integer k ≥ 2, let (i 1 , .., i m ) be a finite sequence with terms chosen from {1, · · · , k}, and assume at least one of the terms in (i 1 , · · · , i m ) appears exactly once. The generalized product of k operators A 1 , ..., A k ∈ B(X) is defined by A 1 ∗ A 2 ∗ · · · ∗ A k = A i ₁ A i ₂ · · · A i m , and includes the usual product and the triple product. We characterize the form of maps from B(X) onto itself satisfying F (ϕ(A 1 ) ∗ · · · ∗ ϕ(A k )) = F (A 1 ∗ · · · ∗ A k ) for all A 1 , · · · , A k ∈ B(X).
author	Bouramdane,Y. Ech-Cherif El Kettani,M. Elhiri,A. Lahssaini,A.
author_facet	Bouramdane,Y. Ech-Cherif El Kettani,M. Elhiri,A. Lahssaini,A.
author_sort	Bouramdane,Y.
title	Maps preserving fixed points of generalized product of operators
title_short	Maps preserving fixed points of generalized product of operators
title_full	Maps preserving fixed points of generalized product of operators
title_fullStr	Maps preserving fixed points of generalized product of operators
title_full_unstemmed	Maps preserving fixed points of generalized product of operators
title_sort	maps preserving fixed points of generalized product of operators
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2020
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000501157
work_keys_str_mv	AT bouramdaney mapspreservingfixedpointsofgeneralizedproductofoperators AT echcherifelkettanim mapspreservingfixedpointsofgeneralizedproductofoperators AT elhiria mapspreservingfixedpointsofgeneralizedproductofoperators AT lahssainia mapspreservingfixedpointsofgeneralizedproductofoperators
_version_	1718439882299277312

Maps preserving fixed points of generalized product of operators

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