Geodesic
Dynamical Systems on Hilbert Modules Over Locally $C^*$-Algebras
Kragujevac Journal of Mathematics, Tome 42 (2018) no. 2, p. 239

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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 
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     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 },
     publisher = {mathdoc},
     volume = {42},
     number = {2},
     year = {2018},
     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/