Covariant completely positive linear maps between locally C*-algebras

Details Covariant completely positive linear maps between locally C*-algebras Covariant completely positive linear maps between locally C*-algebras

2006-09-05

arxiv.org/abs/math/0609149v1

Mathematics

Operator Algebras

13 pages. Houston J. Math. (to appear)

Scientific paper

We prove a covariant version of the KSGNS (Kasparov, Stinespring, Gel'fand,Naimark,Segal) construction for completely positive linear maps between locally $C^{*}$-algebras. As an application of this construction, we show that a covariant completely positive linear map $\rho $ from a locally $C^{*}$-algebra $A$ to another locally $C^{*}$ -algebra $B$ with respect to a locally $C^{*}$-dynamical system $(G,A,\alpha)$ extends to a completely positive linear map on the crossed product $A\times_{\alpha ^{{}}}G$.

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