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, $(A,\QTR{cal}{\phi}),$ 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].