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Journal of Operator Theory

Volume 93, Issue 1, Winter 2025  pp. 115-122.

Upgrading subordination properties in free probability

Authors:  Serban T. Belinschi (1), Hari Bercovici (2)
Author institution: (1) Institut de Mathematiques de Toulouse, UMR 5219, CNRS, France
(2) Department of Mathematics, Indiana University, Bloomington, IN 47405, U.S.A.

Summary:  Belinschi, Mai and Speicher proved a subordination result in the context of free probability in a nontracial $C^*$-probability space. We use a matrix construction to show that the subordination functions thus obtained also satisfy an appropriately modified form of subordination for conditional expectations.

DOI: http://dx.doi.org/10.7900/jot.2022dec2022.2405
Keywords:  analytic subordination, free probability, operator-valued random variables

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Journal of Operator Theory
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