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Gaussian-like von Neumann algebras and noncommutative brownian motion

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Title: Gaussian-like von Neumann algebras and noncommutative brownian motion
Author(s): Avsec, Stephen
Director of Research: Junge, Marius
Doctoral Committee Chair(s): Boca, Florin
Doctoral Committee Member(s): Junge, Marius; Baryshnikov, Yuliy; Athreya, Jayadev S.
Department / Program: Mathematics
Discipline: Mathematics
Degree Granting Institution: University of Illinois at Urbana-Champaign
Degree: Ph.D.
Genre: Dissertation
Subject(s): noncommutative probability von Neumann algebras
Abstract: The $q$-Gaussian von Neumann algebras were first defined and studied by Bo\.{z}ejko and Speicher in connection with noncommutative brownian motion. The main results of the present work is to establish that the $q$-Gaussian von Neumann algebras have the weak* completely contractive approximation property for all $-1 < q < 1$ and any number of generators, and they are strongly solid for all $-1 < q < 1$ and any finite number of generators.
Issue Date: 2012-09-18
URI: http://hdl.handle.net/2142/34412
Rights Information: Copyright 2012 Stephen Avsec
Date Available in IDEALS: 2012-09-18
Date Deposited: 2012-08
 

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