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.
Citation
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
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