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Noncommutative disc algebras for semigroups

Open Access article
 Printed: Apr 1998
  • Kenneth R. Davidson
  • Gelu Popescu
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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 show english descriptions unknown classification 47D25 47D25 - unknown classification 47D25

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