English

Schoenberg correspondence for multifaced independence

Quantum Algebra 2025-09-30 v4

Abstract

We extend the Schoenberg correspondence for universal independences by Sch\"urmann \& Vo{\ss} to the multivariate setting of Manzel \& Sch\"urmann, covering, e.g., Voiculescu's bifreeness as well as Bo{\.z}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''.

Cite

@article{arxiv.2104.02985,
  title  = {Schoenberg correspondence for multifaced independence},
  author = {Malte Gerhold},
  journal= {arXiv preprint arXiv:2104.02985},
  year   = {2025}
}

Comments

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

R2 v1 2026-06-24T00:54:56.117Z