On operator-valued monotone independence

Hasebe, Takahiro; Saigo, Hayato

Nagoya Mathematical Journal, 2014, 215, 151-167

Permalink : https://hdl.handle.net/2115/76038

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Nagoya Math. J215_151-167	pdf	124 KB	371

アクセス権	open access
URI	https://hdl.handle.net/2115/76038
タイトル	On operator-valued monotone independence
著者	e-Rad_Researcher 00633166 著者名 Hasebe, Takahiro
著者	著者名 Saigo, Hayato
言語	英語
発行日	2014-09
収録物名	Nagoya Mathematical Journal
巻(号)	215
ページ	151-167
抄録	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.
資源タイプ	学術雑誌論文
出版タイプ	Accepted Manuscript
権利情報	Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
権利情報	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.
PISSN	0027-7630
EISSN	2152-6842
関連情報 (isVersionOf)	出版社版DOI https://doi.org/10.1215/00277630-2741151