Decomposability of Bimodule Maps - Merdy, Christian Le; Oliveira, Lina (MATHEMATICA SCANDINAVICA, 2016)
Consider a unital C^*-algebra A, a von Neumann algebra M, a unital sub-C^*-algebra CA and a unital *-homomorphism πC→ M. Let uA→ M be a decomposable map (i.e. a linear combination of completely positive maps) which is a C-bimodule map with respect to π. We show that u is a linear combination of C-bimodule completely positive maps if and only if there exists a projection eπ(C)’ such that u is valued in e0.5muMe and eπ(·)e has a completely positive extension A→ e0.5muMe. We also show that this condition is always fulfilled when C has the weak expectation property.