an: Zbl 1201.46050
au: Joi\c ta, Maria
ti: A note on Lebesgue type decomposition for covariant completely positive maps
    on $C^*$-algebras.
la: EN
so: Banach J. Math. Anal. 4, No. 2, 75-86, electronic only (2010).
py: 2010
dt: J
cc: *46L05 46L51 46L40 46L55
ut: covariant completely positive map; Radon-Nikod\'ym derivative; Lebesgue
    decomposition
ab: 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.