Radial multipliers on amalgamated free products of II₁-factors

الأصل · EN

Let Mᵢ be a family of II₁-factors, containing a common II₁-subfactor N, such that [Mᵢ:N] ∈ N₀ for all i. Furthermore, let ϕ N₀ → C. We show that if a Hankel matrix related to ϕ is trace-class, then there exists a unique completely bounded map Mϕ on the amalgamated free product of the Mᵢ with amalgamation over 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.