Matthew Wiersma, Pure Mathematics, University of Waterloo
"Intermediate $C^*$-norms"
It is known that $C^*$-algebras admit unique $C^*$-norms, but this is not true in general for dense $*$-subalgebras of $C^*$-algebras. For example, if $\Gamma$ is a discrete group, then the group ring $\mathbb C[\Gamma]$ may admit more than one $C^*$-norm. Similarly, the algebraic tensor product $\mathcal A\otimes \mathcal B$ of $C^*$-algebras $\mathcal A$ and $\mathcal B$ may admit multiple $C^*$-norms. Each of these examples admits two canonical $C^*$-norms. During this talk, we will investigate $C^*$-norms which fall between these canonical constructions.