Abstract
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 .
Citation
Xiuhong Sun. Yuan Li. "Cone isomorphisms and expressions of some completely positive maps." Ann. Funct. Anal. 8 (1) 27 - 37, February 2017. https://doi.org/10.1215/20088752-3720566
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