Weak Expectation Properties of C*-Algebras and Operator Systems

Abstract

The purpose of this dissertation is two fold. Firstly, we prove a permanence result involving C*-algebras with the weak expectation property. More speci cally, we show that if is an amenable action of a discrete group G on a unital C*-algebra A, then the crossed-product C*-algebra Ao G has the weak expectation property if and only if A has this property. Secondly, the concept of a relatively weakly injective pair of operator systems is introduced and studied, motivated by relative weak injectivity in the C*-algebra category. E. Kirchberg [14] proved that the C*-algebra C (F1) of the free group F1 on countably many generators characterizes relative weak injectivity for pairs of C*-algebras by means of the maximal tensor product. One of the main results in the latter part of this thesis is to show that C (F1) also characterizes relative weak injectivity in the operator system category. A key tool is the theory of operator system tensor products [12, 13].