Explicit construction of universal operator algebras and applications to polynomial factorization

Abstract:

Using the characterization of unital operator algebras developed in [6], we give explicit internal definitions of the free product and the maximal operator-algebra tensor product of operator algebras and of the group operator algebra ${\text {OA}}(G)$ of a discrete semigroup $G$ (if $G$ is a discrete group, then ${\text {OA}}(G)$ coincides with the group ${C^ * }$-algebra ${C^*}(G))$). This approach leads to new factorization theorems for polynomials in one and two variables.