Positive operator bimeasures and a noncommutative generalization
Tom 118 / 1996
Studia Mathematica 118 (1996), 157-168 DOI: 10.4064/sm-118-2-157-168
For C*-algebras A and B and a Hilbert space H, a class of bilinear maps Φ: A× B → L(H), analogous to completely positive linear maps, is studied. A Stinespring type representation theorem is proved, and in case A and B are commutative, the class is shown to coincide with that of positive bilinear maps. As an application, the extendibility of a positive operator bimeasure to a positive operator measure is shown to be equivalent to various conditions involving positive scalar bimeasures, pairs of commuting projection-valued measures or pairs of commuting positive operator measures.