We study noncommutative disc algebras associated to the freeproduct of discrete subsemigroups of $bR^+$. These algebras areassociated to generalized Cuntz algebras, which are shown to besimple and purely infinite. The nonself-adjoint subalgebrasdetermine the semigroup up to isomorphism. Moreover, we establisha dilation theorem for contractive representations of thesesemigroups which yields a variant of the von Neumann inequality.These methods are applied to establish a solution to the truncatedmoment problem in this context.
展开▼
