Illinois Journal of Mathematics

Toeplitz algebras and {$C\sp *$}-algebras arising from reduced (free) group {$C\sp *$}-algebras

Shuang Zhang

Full-text: Open access

Abstract

Assume that $\Gamma$ is a free group on $n$ generators, where $2\le n< +\infty$. Let $\Omega $ be an infinite subset of $\Gamma$ such that $\Gamma \setminus \Omega$ is also infinite, and let $P$ be the projection on the subspace $l^2(\Omega )$ of $l^2(\Gamma )$. We prove that, for some choices of $\Omega$, the C*-algebra $C^*_r(\Gamma ,P)$ generated by the reduced group C*-algebra $C^*_r\Gamma$ and the projection $P$ has exactly two non-trivial, stable, closed ideals of real rank zero. We also give a detailed analysis of the Toeplitz algebra generated by the restrictions of operators in $C^*_r(\Gamma ,P)$ on the subspace $l^2(\Omega )$.

Article information

Source
Illinois J. Math., Volume 48, Number 1 (2004), 199-218.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258136181

Digital Object Identifier
doi:10.1215/ijm/1258136181

Mathematical Reviews number (MathSciNet)
MR2048222

Zentralblatt MATH identifier
1043.46042

Subjects
Primary: 46L05: General theory of $C^*$-algebras
Secondary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]

Citation

Zhang, Shuang. Toeplitz algebras and {$C\sp *$}-algebras arising from reduced (free) group {$C\sp *$}-algebras. Illinois J. Math. 48 (2004), no. 1, 199--218. doi:10.1215/ijm/1258136181. https://projecteuclid.org/euclid.ijm/1258136181


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