Free products of completely positive maps and spectral sets (Q1175007)

Let \((A_ i)_{i\in I}\) be a family of unital \(C^*\)-algebras that contain a common \(C^*\)-algebra \(B\). The main result of the paper under review asserts that the amalgamated product of a family of unital completely positive \(B\)-bimodule maps \(\phi_ i: A_ i\to C\) is completely positive on the ``biggest'' amalgamated free product \(\check\ast_ B A^ i\).