Banach Journal of Mathematical Analysis

On Lebesgue type decomposition for covariant completely positive maps on C*-algebras

Maria Joita

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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 $\left( G,\alpha ,A\right)$ and $u$-covariant completely positive maps from the crossed product $A\times _{\alpha }G$ to $L(H)$, which preserves the Lebesgue decomposition.

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Banach J. Math. Anal., Volume 4, Number 2 (2010), 75-86.

First available in Project Euclid: 7 February 2011

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Zentralblatt MATH identifier

Primary: 46L05: General theory of $C^*$-algebras
Secondary: 46L51: Noncommutative measure and integration 46L40: Automorphisms 46L55: Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]

covariant completely positive map Radon--Nikodym derivative Lebesgue decompositionsolution


Joita, Maria. On Lebesgue type decomposition for covariant completely positive maps on C*-algebras. Banach J. Math. Anal. 4 (2010), no. 2, 75--86. doi:10.15352/bjma/1297117242.

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