The influence of morphisms on Hilbert modules and their dynamical systems
کد مقاله : 1058-SHAA
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
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