Exactness and LLP Results via Operator System Methods

Abstract

In this paper, we employ operator system techniques to investigate structural properties of C*-algebras. In particular, we provide more direct proofs of results concerning exactness and the local lifting property (LLP) of group C${}^{\ast }$-algebras that avoid relying on the traditional heavy machinery of C${}^{\ast }$-algebra theory. Briefly, these methods allow us to deduce that any C*-algebra containing $n$ unitaries whose $\text{ joint numerical radius}$, in the sense defined by \cite{FKP}, is strictly less than $n$, must fail certain of these properties.

Preliminary version. Comments are welcome