paper

Schoenberg correspondence for multifaced independence

arXiv:2104.02985 · doi:10.1016/j.jfa.2025.111212

Abstract

We extend the Schoenberg correspondence for universal independences by Schürmann \& Voß to the multivariate setting of Manzel \& Schürmann, covering, e.g., Voiculescu's bifreeness as well as Bo{ż}ejko \& Speicher's c-free independence. At the same time, we free the proof in the univariate situation from its dependence on Muraki's ``5 Independences Theorem''.

Accepted for publication in Journal of Functional Analysis. 18 pages; changes in v4: streamlined abstract; Remark 2.2 added (subsequent numbering changed); Example 2.4 extended; Remark 4.3 added (subsequent numbering changed); Example 4.7 added; old Section 6 became Problem 5.10, new Section 6 added; minor corrections, reformulations and changes in the acknowledgements

Schoenberg correspondence for multifaced independence · wovepaper