Annals of Functional Analysis

Cone isomorphisms and expressions of some completely positive maps

Xiuhong Sun and Yuan Li

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.afa/1476450345

Digital Object Identifier
doi:10.1215/20088752-3720566

Mathematical Reviews number (MathSciNet)
MR3558302

Zentralblatt MATH identifier
1356.47059

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

Keywords
positive cones completely positive maps trace-class operators

Citation

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. https://projecteuclid.org/euclid.afa/1476450345


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