Exactness and LLP results via operator system methods

Preprint, 2025

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∗-algebras that avoid relying on the traditional heavy machinery of C∗-algebra theory. Briefly, these methods allow us to deduce that any C*-algebra containing n unitaries whose  joint numerical radius, in the sense defined by \cite{FKP}, is strictly less than n, must fail certain of these properties.