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2013 PROJECTIVE COVARIANT REPRESENTATIONS OF LOCALLY $C^*$-DYNAMICAL SYSTEMS
Jaeseong Heo, Un Cig Ji, Young Yi Kim
Taiwanese J. Math. 17(2): 529-544 (2013). DOI: 10.11650/tjm.17.2013.2156

Abstract

As a generalization of covariant completely positive maps, we consider (projective) covariant $\alpha$-completely positive maps between locally $C^*$-algebras. We first study (projective) covariant $J$-representations of locally $C^*$-algebras on Krein modules over locally $C^*$-algebras. Secondly, we construct a covariant KSGNS type representation associated with a covariant $\alpha$-completely positive map on a locally $C^*$-algebra, and then study extensions to a locally $C^*$-crossed product of $\alpha$-completely positive maps on a locally $C^*$-algebra. The results provide (projective) covariant representations of a locally $C^*$-crossed product on a Krein module over a locally $C^*$-algebra.

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Jaeseong Heo. Un Cig Ji. Young Yi Kim. "PROJECTIVE COVARIANT REPRESENTATIONS OF LOCALLY $C^*$-DYNAMICAL SYSTEMS." Taiwanese J. Math. 17 (2) 529 - 544, 2013. https://doi.org/10.11650/tjm.17.2013.2156

Information

Published: 2013
First available in Project Euclid: 10 July 2017

zbMATH: 1286.46058
MathSciNet: MR3044521
Digital Object Identifier: 10.11650/tjm.17.2013.2156

Subjects:
Primary: 46K10 , 46L08
Secondary: 46L55 , 47L60

Keywords: $\alpha$-completely positive map , $J$-representation , Krein module , locally $C^*$-algebra , locally $C^*$-dynamical system , projective representation

Rights: Copyright © 2013 The Mathematical Society of the Republic of China

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