@article{1201.46050,
author="Joi\c ta, Maria",
title="{A note on Lebesgue type decomposition for covariant completely positive
    maps on $C^*$-algebras.}",
language="English",
journal="Banach J. Math. Anal. ",
volume="4",
number="2",
pages="75-86",
year="2010",
abstract="{Summary: We show that there is an affine order isomorphism between
    completely positive maps from a $C^*$-algebra A to the $C^*$-algebra $L(H)$
    of all bounded linear operators on a Hilbert space $H$, $u$-covariant with
    respect to a $C^*$-dynamical system $(G, \alpha , A)$ and $u$-covariant
    completely positive maps from the crossed product $A\times \alpha G$ to
    $L(H)$, which preserves the Lebesgue decomposition.}",
keywords="{covariant completely positive map; Radon-Nikod\'ym derivative;
    Lebesgue decomposition}",
classmath="{*46L05 (General theory of C*-algebras)
46L51 (Noncommutative measure and integration)
46L40 (Automorphisms of C*-algebras)
46L55 (Noncommutative dynamical systems)
}",
}