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

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.