Noncommutative disc algebras for semigroups
Printed: Apr 1998
Kenneth R. Davidson
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.
47D25 - unknown classification 47D25