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

Kirchberg;Module

Liang, Jian

关键词: Kirchberg;    Module;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/78377/LIANG-DISSERTATION-2015.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

In this thesis, we will first follow Kirchberg’s categorical perspective to establish operator-valued WEPand QWEP. We develop similar properties as that in the classical WEP and QWEP, and illustrate therelations with the classical cases by some examples. Then we will discuss the notion of relative WEP inthe context of Hilbert correspondence and investigate the relations between relatively weak injectivityand relative amenablity. Finally we will apply our discoveries to recent results on C∗ -norms, andgenerically find a mechanism to construct a continuum number of C∗ -norms on some tensor productswhich admit infinitely many copies.