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Title:Operator-valued Kirchberg Theory and its connection to tensor norms and correspondences
Author(s):Liang, Jian
Director of Research:Ruan, Zhong-Jin
Doctoral Committee Chair(s):Boca, Florin P.
Doctoral Committee Member(s):Junge, Marius; Kavruk, Ali S.
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(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.
Issue Date:2015-04-20
Type:Thesis
URI:http://hdl.handle.net/2142/78377
Rights Information:Copyright 2015 by Jian Liang
Date Available in IDEALS:2015-07-22
Date Deposited:May 2015


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