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# Noncommutative disc algebras for semigroups

Published:1998-04-01
Printed: Apr 1998
• Kenneth R. Davidson
• Gelu Popescu
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## Abstract

We study noncommutative disc algebras associated to the free product of discrete subsemigroups of $\bbR^+$. These algebras are associated to generalized Cuntz algebras, which are shown to be simple and purely infinite. The nonself-adjoint subalgebras determine the semigroup up to isomorphism. Moreover, we establish a dilation theorem for contractive representations of these semigroups which yields a variant of the von Neumann inequality. These methods are applied to establish a solution to the truncated moment problem in this context.
 MSC Classifications: 47D25 - unknown classification 47D25