On the construction of free random variables
type: Item
instance of: scholarly article
title: On the construction of free random variables
zbMATH Open document ID: 0914.46051
author: Øyvind Ryan
published in: Journal of Functional Analysis
publication date: 1999-06-21T00:00:00Z
full work available at URL: http://hdl.handle.net/10852/42953
review text: The aim of the paper is to investigate the construction of free families of random variables from an initial free family, in a tracial noncommutative probability space. The random variables in this initial free family are multiplied on the left and the right by certain operators from a \(*\)-algebra free from the entire family. Necessary and sufficient conditions are obtained in various cases of the considered problem, and some of them are inspired by similar results and notions comprised by \textit{A. Nica} and \textit{R. Speicher} [Am. J. Math. 118, No. 4, 799-837 (1996; Zbl 0856.46035)].
reviewed by: Neculai Curteanu
Mathematics Subject Classification ID: 46L51
Mathematics Subject Classification ID: 46L53
Mathematics Subject Classification ID: 46L54
Mathematics Subject Classification ID: 60B99
zbMATH DE Number: 1216762
zbMATH Keywords: multiplication by certain operators of a free family of random variables
zbMATH Keywords: tracial noncommutative probability space
MaRDI profile type: Publication
OpenAlex ID: W1991408394
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DOI: 10.1006/JFAN.1997.3209
description: scientific article; zbMATH DE number 1216762