Geodesic
Dynamical Systems on Hilbert Modules Over Locally $C^*$-Algebras
Kragujevac Journal of Mathematics, Tome 42 (2018) no. 2, p. 239 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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Let $\mathcal{A}$ be a locally $C^*$-algebra and $S(\mathcal{A})$ be the family of continuous $C^*$-seminorms and let $\mathcal{E}$ be a Hilbert $\mathcal{A}$-module. We prove that every dynamical system of unitary operators on $\mathcal{E}$ defines a dynamical system of automorphisms on the compact operators on $\mathcal{E}$ and show that under certain conditions, the converse is true. We define a generalized derivation on $\mathcal{E}$ and prove that if $\mathcal{E}$ is a full Hilbert $\mathcal{A}$-module and $\delta : \mathcal{E} \to \mathcal{E}$ is a bounded generalized derivation, then $\delta_p: \mathcal{E}_p \to \mathcal{E}_p$ is a generalized derivation on the Hilbert module $\mathcal{E}_p$ over the $C^*$-algebra $\mathcal{A}_p$ for each $p \in S(\mathcal{A})$.
Classification : 46L08 46L57, 46D60
Keywords: Locally $C^*$-algebra, dynamical system, generalized derivation 
@article{KJM_2018_42_2_a6,
     author = {L. Naranjani and M. Hassani and M. Amyari},
     title = {Dynamical {Systems} on {Hilbert} {Modules} {Over} {Locally} $C^*${-Algebras}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {239 },
     year = {2018},
     volume = {42},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2018_42_2_a6/}
}
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L. Naranjani; M. Hassani; M. Amyari. Dynamical Systems on Hilbert Modules Over Locally $C^*$-Algebras. Kragujevac Journal of Mathematics, Tome 42 (2018) no. 2, p. 239 . http://geodesic.mathdoc.fr/item/KJM_2018_42_2_a6/