On operator-valued monotone independence


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Please use this identifier to cite or link to this item:http://hdl.handle.net/2115/76038

Title:	On operator-valued monotone independence
Authors:	Hasebe, Takahiro Browse this author →KAKEN DB
Authors:	Saigo, Hayato Browse this author
Issue Date:	Sep-2014
Journal Title:	Nagoya Mathematical Journal
Volume:	215
Start Page:	151
End Page:	167
Publisher DOI:	10.1215/00277630-2741151
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 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.
Rights:	This article has been published in a revised form in Nagoya Mathematical Journal http://dx.doi.org/10.1215/00277630-2741151. This version is published under a Creative Commons CC-BY-NC-ND. No commercial re-distribution or re-use allowed. Derivative works cannot be distributed. © 2014 by The Editorial Board of the Nagoya Mathematical Journal.
Rights:	https://creativecommons.org/licenses/by-nc-nd/4.0/
Type:	article (author version)
URI:	http://hdl.handle.net/2115/76038
Appears in Collections:	理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 長谷部高広

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