Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 8, Number 1 (2017), 27-37.
Cone isomorphisms and expressions of some completely positive maps
Let , and be the set of all bounded linear operators, compact operators, and trace-class operators on the Hilbert space . The cone of all completely positive maps from into and all normal completely positive maps from into is denoted by and , respectively. In this note, the order structures of the positive cones and are investigated. First, we show that , , and are cone-isomorphic. Then we give the operator sum representation for the map .
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
Permanent link to this document
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
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