A Banach Algebra Approach To Amalgamated R- and S-transforms

2004/06/09 by L. Aagaard, Aagaard, L.
Mathematics · #46L54 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L54

paper · pdf · doi:10.48550/arxiv.math/0406167

22 pages

arxiv created 2004/06/09 · arxiv updated 2009/12/01

Abstract

We give a Banach algebra approach to the additiveness property of Voiculescu's amalgamated R-transform. We also define an amalgamated S-transform and prove that it is multiplicative on products of amalgamated free random variables when the algebra of amalgamation is commutative.

Related

• On the S-transform over a Banach algebra
• R-transform Theory On a Tower of Amalgamated Noncommutative Probability Spaces
• On the multiplication of operator-valued c-free random variables
• On the twisted factorization of the T-transform
• Almost Commutative Probability Theory