Annals of Functional Analysis

Cone isomorphisms and expressions of some completely positive maps

Xiuhong Sun and Yuan Li

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Let B(H), K(H) and T(H) be the set of all bounded linear operators, compact operators, and trace-class operators on the Hilbert space H. The cone of all completely positive maps from K(H) into T(K) and all normal completely positive maps from B(K) into T(H) is denoted by CP(K(H),T(K)) and NCP(B(K),T(H)), respectively. In this note, the order structures of the positive cones CP(K(H),T(K)) and NCP(B(K),T(H)) are investigated. First, we show that CP(K(H),T(K)), NCP(B(K),T(H)), and T(K⊗H)+ are cone-isomorphic. Then we give the operator sum representation for the map ΦCP(K(H),T(K)).

Article information

Ann. Funct. Anal., Volume 8, Number 1 (2017), 27-37.

Received: 19 February 2016
Accepted: 21 May 2016
First available in Project Euclid: 14 October 2016

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47L05: Linear spaces of operators [See also 46A32 and 46B28]
Secondary: 47L50: Dual spaces of operator algebras

positive cones completely positive maps trace-class operators


Sun, Xiuhong; Li, Yuan. Cone isomorphisms and expressions of some completely positive maps. Ann. Funct. Anal. 8 (2017), no. 1, 27--37. doi:10.1215/20088752-3720566.

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