On operator-valued monotone independence

Takahiro Hasebe; Hayato Saigo

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arXiv · 1306.0137

On operator-valued monotone independence

Takahiro Hasebe·Hayato Saigo

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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.

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Takahiro Hasebe, Hayato Saigo. 2013-06-01. On operator-valued monotone independence. https://arxiv.org/abs/1306.0137

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