Nagoya Mathematical Journal

On operator-valued monotone independence

Takahiro Hasebe and Hayato Saigo

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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 the central limit theorem for the 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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Nagoya Math. J., Volume 215 (2014), 151-167.

First available in Project Euclid: 22 July 2014

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Zentralblatt MATH identifier

Primary: 46L53: Noncommutative probability and statistics
Secondary: 46L54: Free probability and free operator algebras 13F25: Formal power series rings [See also 13J05] 06A07: Combinatorics of partially ordered sets


Hasebe, Takahiro; Saigo, Hayato. On operator-valued monotone independence. Nagoya Math. J. 215 (2014), 151--167. doi:10.1215/00277630-2741151.

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