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

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Liang, Jian

Contributors dc:contributor

• Ruan, Zhong-Jin
• Boca, Florin P.
• Junge, Marius
• Kavruk, Ali S.

• Kirchberg
• Module

Statement dc:rights

• Copyright 2015 by Jian Liang

Language dc:language

en

Handle dc:identifier

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

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/78377