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

Abstract

In this paper, we will consider a noncommutative probability space, $(T,E),$ over a Toeplitz matricial algebra $B=\QTR{cal}{C}^{N},$ for $N\in \QTR{Bbb}{N}$, induced by a (scalar-valued) noncommutative probability space, $(A,\QTR{cal}ϕ),$ with a suitable $B$-functional, $E:T\to B,$ defined by $\varphi .$ 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].

46 pages