Dilations for $C^ast$-dynamical systems with abelian groups on Hilbert $C^ast$-modules

Document Type: Research Paper

Authors

College of Mathematics and Information Science‎, ‎Shaanxi Normal University‎, ‎Xi'an‎, ‎Shaanxi‎, ‎710062‎, ‎P‎.‎R‎. ‎China.

Abstract

‎In this paper we investigate the dilations of completely positive definite representations‎ ‎of \(C^\ast\)-dynamical systems with abelian groups on Hilbert \(C^\ast\)-modules‎. ‎We show that if \((\mathcal{A}‎, ‎G,\alpha)\) is a \(C^\ast\)-dynamical system with \(G\) an abelian group‎, ‎then every completely positive definite covariant representation \((\pi,\varphi,E)\) of \((\mathcal{A}‎, ‎G,\alpha)\) on a Hilbert \(C^\ast\)-module \(E\) admits an unitary dilation $((\hat{\pi},\hat{\varphi},\hat{E})).$

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