Radial multipliers on amalgamated free products of II_1-factors

Abstract

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 $\varphi :{\mathbb{N}}_0\to \mathbb{C}$. We show that if a Hankel matrix related to $\varphi$ is trace-class, then there exists a unique completely bounded map $M_{\varphi }$ 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 $C^{\ast }$- and von Neumann algebras.

13 pages, some adjustments (v2), restricted to integer-index case to avoid problem (v3), updated references (v3)

References in corpus (1)

• Radial multipliers on reduced free products of operator algebras

Cited by in corpus (1)

• Radial multipliers on arbitrary amalgamated free products of finite von Neumann algebras