On operator-valued monotone independence. (September 2014)

• Record Type: Journal Article
• Authors: Hasebe, Takahiro; Saigo, Hayato
• Is Part Of: Nagoya mathematical journal. Volume 215(2014)
• Page Start: 151
• Page End: 167
• Publication Date: 2014-09
• Subjects: 46L53, -- 46L54, -- 13F25, -- 06A07; Mathematics -- Periodicals; Mathématiques -- Périodiques; Mathematics; Wiskunde; Electronic journals; Periodicals; 510.5
• DOI: 10.1215/00277630-2741151
• Languages: English
• ISSNs: 0027-7630

Abstract

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.