Nonlinear fixed points preservers

Autor: Y. Bouramdane, M. Ech-Cherif El Kettani, A. Lahssaini
Rok vydání: 2020
Předmět:
Zdroj: Rendiconti del Circolo Matematico di Palermo Series 2. 70:1269-1276
ISSN: 1973-4409
0009-725X
DOI: 10.1007/s12215-020-00558-7
Popis: Let $${\mathcal {B}}(X)$$ be the algebra of all bounded linear operators on an infinite dimensional complex Banach space X. For $$A\in {\mathcal {B}}(X)$$ , let F(A) be the set of all fixed points of A. For an integer $$k\ge 2$$ , let $$(i_1,\dots ,i_m)$$ be a finite sequence with terms chosen from $$\{1,\dots ,k\}$$ and assume that at least one of the terms in $$(i_1,\dots ,i_m)$$ appears exactly once. The generalized product of k operators $$A_1,\dots ,A_k \in {\mathcal {B}}(X)$$ is defined by $$\begin{aligned} A_1*A_2*\cdots *A_k=A_{i_{1}}A_{i_{2}}\dots A_{i_{m}} \end{aligned}$$ and includes the usual product and the triple product. In this paper we characterize the form of surjective maps from $${\mathcal {B}}(X)$$ into itself satisfying $$\begin{aligned} \dim F(\phi (A_{1})*\dots *\phi (A_{k}))=\dim F(A_{1}*\cdots *A_{k}) \end{aligned}$$ for all $$A_1,\dots ,A_k \in {\mathcal {B}}(X)$$ .
Databáze: OpenAIRE
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