Amalgamated R-diagonal Pairs

A note on unital full amalgamated free products of quasi-diagonal C*-algebras

In the paper, we consider the question whether a unital full amalgamated free product of quasidiagonal C*-algebras is quasidiagonal again. We give a sufficient condition such that a unital full amalgamated free product of quasidiagonal C*-algebras with amalgamation over a finite dimensional C*- algebra is quasidiagonal. Applying this result, we conclude that a unital full free product of two AF algebras with amalgamation over a finite-dimensional C*-algebra is AF if there are faithful tracial states on each of these two AF algebras such that the restrictions on the common subalgebra agree.

Random Variables in Graph W*-Probability Spaces

In [16], we observed the graph W*-probability theory. In this paper, we will review [16] and introduce special amalgamated random variables in this amalgamated W*-probability space. In particular, we will observe the amalgamated semicircularity, amalgamated evenness and amalgamated R-diagonality. As an example, we will compute the trivial moments and trivial cumulants of the generating operator of the graph W*-algebra.

Diagonal Compressed Random Variables in a Graph W*-probability Spaces

In [15] and [16], we constructed a graph W*-probability space over its diagonal subalgebra. To study this strudture is a good example of Speicher's amalgamated W*-probability spaces. In this paper, we will observe the diagonal compressed random variables. we will compute the moments and cumulants of them and we will show that the freeness on diagonal compressed random variables in the graph W*-probability space is preserved by that of (uncompressed) random variables.

对角维数与中间子\(C^*\)-代数

Diagonal dimension and intermediate sub-C*-algebras

研究对角维数的有限性与中间子\(C^*\)-代数的关系，通过获取中间子\(C^*\)-代数与对角组成的对的对角维数上界，推广了阿奇博尔德和库姆简关于\(AF\)-对角中间子代数的定理。

$R$-diagonal and $η$-diagonal Pairs of Random Variables

This paper is devoted to studying $R$-diagonal and $η$-diagonal pairs of random variables. We generalize circular elements to the bi-free setting, defining bi-circular element pairs of random variables, which provide examples of $R$-diagonal pairs of random variables. Formulae are given for calculating the distributions of the product pairs of two $*$-bi-free $R$-diagonal pairs. When focusing on pairs of left acting operators and right acting operators from finite von Neumann algebras in the standard form, we characterize $R$-diagonal pairs in terms of the $*$-moments of the random variables, …

关于双自由概率中双R-对角算子对的性质

On Bi-R-Diagonal Pairs of Operators

研究双自由概率中R-对角算子的性质，分析双R-对角算子对的乘积及幂的性质，探讨其联合分布的不变性及等价刻画。