Let $\mathcal{ M}_i$ be a family of $\mathrm{ II}_1$-factors, containing a common $\mathrm{ II}_1$-subfactor $\mathcal{ N}$, such that $[\mathcal{ M}_i:\mathcal{ N}] \in \mathbb{ N}_0$ for all $i$. Furthermore, let $\phi \colon \mathbb{ N}_0 \to \mathbb{ C}$. We show that if a Hankel matrix related to $\phi$ is trace-class, then there exists a unique completely bounded map $M_\phi$ on the amalgamated free product of the $\mathcal{ M}_i$ with amalgamation over $\mathcal{ N}$, which acts as an radial multiplier. Hereby we extend a result of U. Haagerup and the author for radial multipliers on reduced free products of unital $C^*$- and von Neumann algebras.
Categories: math.OA