Nagoya Mathematical Journal

On operator-valued monotone independence

Takahiro Hasebe and Hayato Saigo

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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.

Article information

Source
Nagoya Math. J. Volume 215 (2014), 151-167.

Dates
First available in Project Euclid: 22 July 2014

Permanent link to this document
http://projecteuclid.org/euclid.nmj/1406039894

Digital Object Identifier
doi:10.1215/00277630-2741151

Mathematical Reviews number (MathSciNet)
MR3263527

Zentralblatt MATH identifier
1291.81350

Subjects
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

Citation

Hasebe, Takahiro; Saigo, Hayato. On operator-valued monotone independence. Nagoya Math. J. 215 (2014), 151--167. doi:10.1215/00277630-2741151. http://projecteuclid.org/euclid.nmj/1406039894.


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References

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Nagoya Mathematical Journal

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