Operator-valued Kirchberg Theory and its connection to tensor norms and correspondences
Liang, Jian
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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
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.
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