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http://dx.doi.org/10.4134/BKMS.2010.47.6.1275

WIENER-HOPF C*-ALGEBRAS OF STRONGL PERFORATED SEMIGROUPS  

Jang, Sun-Young (DEPARTMENT OF MATHEMATICS UNIVERSITY OF ULSAN)
Publication Information
Bulletin of the Korean Mathematical Society / v.47, no.6, 2010 , pp. 1275-1283 More about this Journal
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($\mathbb{Z}$, M) of subsemigroup generating the integer group $\mathbb{Z}$ is isomorphic to the Toeplitz algebra, but W($\mathbb{Z}$, M) does not have the uniqueness property except the case M = $\mathbb{N}$.
Keywords
left regular isometric representation; Wiener-Hopf $C^*$-algebra unperforated semigroup; Toeplitz algebra;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By Web Of Science : 0  (Related Records In Web of Science)
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