University of Illinois Urbana-Champaign

Operator-valued Kirchberg Theory and its connection to tensor norms and correspondences

Liang, Jian

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LIANG-DISSERTATION-2015.pdf

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https://hdl.handle.net/2142/78377

Description

Title
Operator-valued Kirchberg Theory and its connection to tensor norms and correspondences
Author(s)
Liang, Jian
Issue Date
2015-04-20
Director of Research (if dissertation) or Advisor (if thesis)
Ruan, Zhong-Jin
Doctoral Committee Chair(s)
Boca, Florin P.
Committee Member(s)
  • Junge, Marius
  • Kavruk, Ali 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
2015-07-22T22:16:42Z
Keyword(s)
  • Kirchberg
  • Module
Abstract
In this thesis, we will first follow Kirchberg’s categorical perspective to establish operator-valued WEP and QWEP. We develop similar properties as that in the classical WEP and QWEP, and illustrate the relations with the classical cases by some examples. Then we will discuss the notion of relative WEP in the context of Hilbert correspondence and investigate the relations between relatively weak injectivity and relative amenablity. Finally we will apply our discoveries to recent results on C∗ -norms, and generically find a mechanism to construct a continuum number of C∗ -norms on some tensor products which admit infinitely many copies.
Graduation Semester
2015-5
Type of Resource
text
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http://hdl.handle.net/2142/78377
Copyright and License Information
Copyright 2015 by Jian Liang

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