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

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

2001-01-17

arxiv.org/abs/math/0101146v1

Mathematics

Operator Algebras

Scientific paper

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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