TY - JOUR ID - 1026 TI - Dilations for $C^ast$-dynamical systems with abelian groups on Hilbert $C^ast$-modules JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - Wang, Z. AU - Zhang, J. AD - College of Mathematics and Information Science‎, ‎Shaanxi Normal University‎, ‎Xi'an‎, ‎Shaanxi‎, ‎710062‎, ‎P‎.‎R‎. ‎China. Y1 - 2017 PY - 2017 VL - 43 IS - 5 SP - 1313 EP - 1321 KW - Dilation KW - covariant representation KW - $C^ast$-dynamical system KW - Hilbert $C^ast$-module DO - N2 - ‎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 $((\hat{\pi},\hat{\varphi},\hat{E})).$ UR - http://bims.iranjournals.ir/article_1026.html L1 - http://bims.iranjournals.ir/article_1026_7331f04fa6ff4e9f75048878a153860b.pdf ER -