Amalgamated R-transform Theory on Toeplitz-Probability Spaces over Toeplitz Matricial Algebras

2004/05/06 by Ilwoo Cho, Cho, Ilwoo
Mathematics · #47-xx #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Random Matrices and Applications #math.FA #math.OA #msc:47-xx

paper · pdf · doi:10.48550/arxiv.math/0405106

46 pages

arxiv created 2004/05/06 · openalex publication_date 2004/05/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we will consider a noncommutative probability space, (T,E), over a Toeplitz matricial algebra B=\QTRcalC^N, for N∈ \QTRBbbN, induced by a (scalar-valued) noncommutative probability space, (A,\QTRcalϕ), with a suitable B-functional, E:T→ B, defined by ϕ. On this framework, we will observe amalgamated R-transform calculus with respect to a B-functional, E. The technique and idea are came from those in [12] and Free Probability of type B studied in [31].

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