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- Title
Strong convergence for reduced free products.
- Authors
Pisier, Gilles
- Abstract
Using an inequality due to Ricard and Xu, we give a different proof of Paul Skoufranis's recent result showing that the strong convergence of possibly non-commutative random variables is stable under reduced free product with a fixed non-commutative random variable . In fact we obtain a more general fact: assuming that the families and are ∗-free as well as their limits (in moments) and , the strong convergences and imply that of to . Phrased in more striking language: the reduced free product is 'continuous' with respect to strong convergence. The analogue for weak convergence (i.e. convergence of all moments) is obvious. Our approach extends to the amalgamated free product, left open by Skoufranis.
- Subjects
MATHEMATICAL equivalence; STOCHASTIC convergence; FREE products (Group theory); RANDOM variables; NONCOMMUTATIVE differential geometry
- Publication
Infinite Dimensional Analysis, Quantum Probability & Related Topics, 2016, Vol 19, Issue 2, p-1
- ISSN
0219-0257
- Publication type
Article
- DOI
10.1142/S0219025716500089