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.