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, $E:T\to B,$ defined by $\phi .$ 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].
Categories: math.OA math.FA