Gaussian-like von Neumann algebras and noncommutative brownian motion
Avsec, Stephen
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https://hdl.handle.net/2142/34412
Description
Title
Gaussian-like von Neumann algebras and noncommutative brownian motion
Author(s)
Avsec, Stephen
Issue Date
2012-09-18T21:15:39Z
Director of Research (if dissertation) or Advisor (if thesis)
Junge, Marius
Doctoral Committee Chair(s)
Boca, Florin
Committee Member(s)
Junge, Marius
Baryshnikov, Yuliy
Athreya, Jayadev S.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(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.
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