2026-09-21T05:10:24Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/78377 2023-07-11 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Ruan, Zhong-Jin Boca, Florin P. Junge, Marius Kavruk, Ali S. Liang, Jian 2015-07-22T22:16:42Z 2015-07-22T22:16:42Z 2015-05 2015-04-20 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. Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2015-07-22 without embargo terms The student, Jian Liang, accepted the attached license on 2015-04-13 at 17:23. The student, Jian Liang, submitted this Dissertation for approval on 2015-04-13 at 17:31. This Dissertation was approved for publication on 2015-04-20 at 08:35. DSpace SAF Submission Ingestion Package generated from Vireo submission #7841 on 2015-07-22 at 10:31:54 Made available in DSpace on 2015-07-22T22:16:42Z (GMT). No. of bitstreams: 2 LIANG-DISSERTATION-2015.pdf: 527078 bytes, checksum: 391658c93b8aaa985e0fe120d7325e2f (MD5) LICENSE.txt: 4207 bytes, checksum: b4355ed4f47f685461bf2c17ed7964ea (MD5) Previous issue date: 2015-04-20 application/pdf http://hdl.handle.net/2142/78377 en Copyright 2015 by Jian Liang Kirchberg Module Operator-valued Kirchberg Theory and its connection to tensor norms and correspondences text text 2015-5 Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.