University of Illinois Urbana-Champaign

Gaussian-like von Neumann algebras and noncommutative brownian motion

Avsec, Stephen

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avsec_stephen.pdf

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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
Date of Ingest
2012-09-18T21:15:39Z
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.
Graduation Semester
2012-08
Permalink
http://hdl.handle.net/2142/34412
Copyright and License Information
Copyright 2012 Stephen Avsec

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