WIENER-HOPF C*-ALGEBRAS OF STRONGL PERFORATED SEMIGROUPS

Title & Authors
WIENER-HOPF C*-ALGEBRAS OF STRONGL PERFORATED SEMIGROUPS
Jang, Sun-Young;

Abstract
If the Wiener-Hopf $\small{C^*}$-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 $\small{C^*}$-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 $\small{C^*}$-algebra W($\small{\mathbb{Z}}$, M) of subsemigroup generating the integer group $\small{\mathbb{Z}}$ is isomorphic to the Toeplitz algebra, but W($\small{\mathbb{Z}}$, M) does not have the uniqueness property except the case M
Keywords
left regular isometric representation;Wiener-Hopf $\small{C^*}$-algebra unperforated semigroup;Toeplitz algebra;
Language
English
Cited by
References
1.
L. A. Coburn, The \$C^{\ast}-algebra\$ generated by an isometry. II, Trans. Amer. Math. Soc. 137 (1969), 211-217.

2.
J. Cuntz, Simple \$C^{\ast}-algebras\$ generated by isometries, Comm. Math. Phys. 57 (1977), no. 2, 173-185.

3.
K. R. Davidson, E. Katsoulis, and D. R. Pitts, The structure of free semigroup algebras, J. Reine Angew. Math. 533 (2001), 99-125.

4.
R. G. Douglas, On the \$C^{\ast}-algebra\$ of a one-parameter semigroup of isometries, Acta Math. 128 (1972), no. 3-4, 143-151.

5.
G. A. Elliott, Dimension groups with torsion, Internat. J. Math. 1 (1990), no. 4, 361-380.

6.
S. Y. Jang, Reduced crossed products by semigroups of automorphisms, J. Korean Math. Soc. 36 (1999), no. 1, 97-107.

7.
S. Y. Jang, Generalized Toeplitz algebra of a certain non-amenable semigroup, Bull. Korean Math. Soc. 43 (2006), no. 2, 333-341.

8.
M. Laca and I. Raeburn, Semigroup crossed products and the Toeplitz algebras of non-abelian groups, J. Funct. Anal. 139 (1996), no. 2, 415-440.

9.
P. Muhly and J. Renault, \$C^{\ast}-algebras\$ of multivariable Wiener-Hopf operators, Trans. Amer. Math. Soc. 274 (1982), no. 1, 1-44.

10.
G. J. Murphy, Crossed products of \$C^{\ast}-algebras\$ by semigroups of automorphisms, Proc. London Math. Soc. (3) 68 (1994), no. 2, 423-448.

11.
A. Nica, Some remarks on the groupoid approach to Wiener-Hopf operators, J. Operator Theory 18 (1987), no. 1, 163-198.

12.
A. Nica, \$C^{\ast}-algebras\$ generated by isometries and Wiener-Hopf operators, J. Operator Theory 27 (1992), no. 1, 17-52.

13.
G. K. Pedersen, \$C^{\ast}-Algebras\$ and Their Automorphism Groups, Academic Press, Inc., London-New York, 1979.

14.
M. Rordam, The stable and the real rank of Z-absorbing \$C^{\ast}-algebras\$, Internat. J. Math. 15 (2004), no. 10, 1065-1084.

15.
M. Rordam, Structure and classification of \$C^{\ast}-algebras\$, International Congress of Mathematicians. Vol. II, 1581-1598, Eur. Math. Soc., Zurich, 2006.