| The influence of morphisms on Hilbert modules and their dynamical systems |
| کد مقاله : 1058-SHAA |
| نویسندگان |
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میثم مصدق * گروه ریاضی دانشگاه آزاد اسلامی واحد لارستان |
| چکیده مقاله |
| In this paper, we establish some conditions under which a morphism of Hilbert modules acts on a (full) Hilbert $A$-module and implements a different (full) Hilbert $B$-module. We also, investigate the effects of unitary operators on dense subspaces of full Hilbert modules, (core of) generalized derivations, and also, (ground) states. Let $phi:Ato B$ be an injective morphism of $C^*$-algebras and $T$ be a surjective $phi$-morphism from a full Hilbert $A$-module $M$ onto a full Hilbert $B$-module $N.$ Introducing the notion of approximately inner generalized dynamical system on Hilbert $C^*$-modules, we show that each (approximately inner) generalized dynamical system on $M$ can be transferred to a (an approximately inner) generalized dynamical system on $N$ by $T,$ and the associated $C^*$-dynamical system on $B$ is exactly the $C^*$-dynamical system transferred by $phi.$ Finally, we characterize the form of a generalized dynamical system on a Cartesian product of two Hilbert $C^*$-modules and as an application of discussed concepts, we demonstrate a generalized dynamical system which is not approximately inner. |
| کلیدواژه ها |
| $C^*$-Dynamical systems, generalized derivation, Hilbert $C^*$-module, unitary operator |
| وضعیت: پذیرفته شده برای ارائه شفاهی |