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


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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Takahiro Hasebe. Hayato Saigo. "On operator-valued monotone independence." Nagoya Math. J. 215 151 - 167, September 2014.


Published: September 2014
First available in Project Euclid: 22 July 2014

zbMATH: 1291.81350
MathSciNet: MR3263527
Digital Object Identifier: 10.1215/00277630-2741151

Primary: 46L53
Secondary: 06A07 , 13F25 , 46L54

Rights: Copyright © 2014 Editorial Board, Nagoya Mathematical Journal

Vol.215 • September 2014
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