Maps preserving fixed points of generalized product of operators
| Autor: | A. Lahssaini, M. Ech-Cherif El Kettani, A. Elhiri, Youssef Bouramdane |
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| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Preserver problems
General Mathematics Linear operators Banach space 010103 numerical & computational mathematics Fixed point 01 natural sciences Finite sequence 010101 applied mathematics Combinatorics Integer Triple product Bounded function Product (mathematics) 0101 mathematics Generalized product Mathematics |
| Zdroj: | Proyecciones (Antofagasta) v.39 n.5 2020 SciELO Chile CONICYT Chile instacron:CONICYT |
| Popis: | 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). |
| Databáze: | OpenAIRE |
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