Weak Expectation Properties of C*-Algebras and Operator Systems

Bhattacharya, Angshuman
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Faculty of Graduate Studies and Research, University of Regina

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].

A Thesis Submitted to the Faculty of Graduate Studies and Research in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Mathematics, University of Regina. vii, 91 p.