Fixed points of dual quantum operations

Let ϕA be a normal completely positive map on B(H) with Kraus operators . Denote M the subset of normal completely positive maps by . In this note, the relations between the fixed points of ϕA and are investigated. We obtain that , where K(H) is the set of all compact operators on H and is the dual of ϕA∈M. In addition, we show that the map is a bijection on M.