Alina Kościukiewicz
Unique Trace Property for Reduced $L^p$-Group Algebras
A trace on a Banach algebra $A$ is a unital contractive functional $\tau:A\to\mathbb{C}$, such that $\tau(ab)=\tau(ba)$ for all $a,b\in A$. If there is exactly one trace on $A$, we say that $A$ has the unique trace. The $L^p$-group algebra is the generalisation of a $C^*$-algebra. We obtain it by the same construction, but instead of representing the Banach algebra $\ell^1(G)$ on the Hilbert space $\ell^2(G)$, we represent it on its "tilted" version $\ell^p(G)$ for all $p\in[1,\infty]$. In the poster, I present theorems concerning the uniqueness of the trace of $L^p$-group algebras and prove a lemma by means of which we obtain the unique trace characterisation.
