WIENER-HOPF C*-ALGEBRAS OF STRONGLY PERFORATED SEMIGROUPS
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If the Wiener-Hopf C*-algebra W(G, M) for a discrete group G with a semigroup M has the uniqueness property, then the structure of it is to some extent independent of the choice of isometries on a Hilbert space. In this paper we show that if the Wiener-Hopf C*-algebra W(G, M) of a partially ordered group G with the positive cone M has the uniqueness property, then (G, M) is weakly unperforated. We also prove that the Wiener-Hopf C*-algebra W(Z, M) of subsemigroup M generating the integer group Z is isomorphic to the Toeplitz algebra, but W(Z, M) does not have the uniqueness property except the case M = N.
Abstract
If the Wiener-Hopf C*-algebra W(G, M) for a discrete group G with a semigroup M has the uniqueness property, then the structure of it is to some extent independent of the choice of isometries on a Hilbert space. In this paper we show that if the Wiener-Hopf C*-algebra W(G, M) of a partially ordered group G with the positive cone M has the uniqueness property, then (G, M) is weakly unperforated. We also prove that the Wiener-Hopf C*-algebra W(Z, M) of subsemigroup M generating the integer group Z is isomorphic to the Toeplitz algebra, but W(Z, M) does not have the uniqueness property except the case M = N.
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