THE $ C^*$-ALGEBRA $\mathcal{T}_m$ AS A CROSSED PRODUCT
DOI:
https://doi.org/10.46991/PSYU:A/2014.48.3.024Keywords:
index of monomial, coefficient algebra, crossed product, finitely representable, Toeplitz algebra, $C^*$-algebra, transfer operatorAbstract
In this paper we consider the $ C^*$-subalgebra $\mathcal{T}_m$ of the Toeplitz algebra $\mathcal{T}$ generated by monomials, which have an index divisible by $m$. We present the algebra $\mathcal{T}_m$ as a crossed product: $\mathcal{T}_m=\varphi(\mathcal{A})\times_{\delta_m}\mathbb{Z}$, where $\mathcal{A}=C_0(\mathbb{Z}_+)\oplus \mathbb{C}I$ is $ C^*$-algebra of all continuous functions on $\mathbb{Z}_+$, which have a finite limit at infinity. In the case $m=1$ we obtain that $\mathcal{T}=\varphi(\mathcal{A})\times_{\delta_1}\mathbb{Z}$, which is an analogue of Coburn's theorem.
Downloads
Published
2014-11-03
How to Cite
Hovsepyan, K. (2014). THE $ C^*$-ALGEBRA $\mathcal{T}_m$ AS A CROSSED PRODUCT. Proceedings of the YSU A: Physical and Mathematical Sciences, 48(3 (235), 24–30. https://doi.org/10.46991/PSYU:A/2014.48.3.024
Issue
Section
Mathematics
License
Copyright (c) 2014 Proceedings of the YSU
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.