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
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Acceso en línea:http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000501157
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Sumario: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).