A Characterization of Freeness by a Factorization Property of R-transform

2001/01/17 by Nica, Alexandru, Shlyakhtenko, Dimitri, Speicher, Roland
#46L54 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.math/0101146

Abstract

Let M be a B-probability space. Assume that B itself is a D-probability space; then M can be viewed as a D-probability space as well. Let X be in M. We characterize freeness of X from B with amalgamation over D in terms of a certain factorization condition linking the B-valued and D-valued R-transforms of X. We give an application to random matrices.

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