Invariant projections for operators that are free over the diagonal

2018/11/09 by Serban T. Belinschi, Belinschi, Serban · 1 citation
Computer Science · Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Operator Algebras (math.OA) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1811.03816

openalex publication_date 2018/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Motivated by recent work of Au, Cébron, Dahlqvist, Gabriel, and Male, we study regularity properties of the distribution of a sum of two selfad-joint random variables in a tracial noncommutative probability space which are free over a commutative algebra. We give a characterization of the invariant projections of such a sum in terms of the associated subordination functions.

Citations

• The free field: zero divisors, Atiyah property and realizations via unbounded operators
• Hölder Continuity of Cumulative Distribution Functions for Noncommutative Polynomials under Finite Free Fisher Information

Cited by

• The atoms of the free additive convolution of two operator-valued distributions

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