A similarity degree characterization of nuclear $C^*$-algebras
Abstract
Description
We show that a $C^*$-algebra $A$ is nuclear iff there is a constant $K$ and $α<3$ such that, for any bounded homomorphism $u\colon A \to B(H)$, there is an isomorphism $ξ\colon H\to H$ satisfying $\|ξ^{-1}\|\|ξ\| \le K\|u\|^α$ and such that $ ξ^{-1} u(.) ξ$ is a $*$-homomorphism. In other words, an infinite dimensional $A$ is nuclear iff its length (in ths sense of our previous work on the Kadison similarity problem) is equal to 2.
This latest version has minor corrections
This latest version has minor corrections