On operator-valued monotone independence
Operator Algebras
2014-09-09 v2
Abstract
We investigate operator-valued monotone independence, a noncommutative version of independence for conditional expectation. First we introduce operator-valued monotone cumulants to clarify the whole theory and show the moment-cumulant formula. As an application, one can obtain an easy proof of Central Limit Theorem for operator-valued case. Moreover, we prove a generalization of Muraki's formula for the sum of independent random variables and a relation between generating functions of moments and cumulants.
Cite
@article{arxiv.1306.0137,
title = {On operator-valued monotone independence},
author = {Takahiro Hasebe and Hayato Saigo},
journal= {arXiv preprint arXiv:1306.0137},
year = {2014}
}
Comments
Proof of Theorem 3.4 is explained