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1. CMB 2005 (vol 48 pp. 607)

Park, Efton
Toeplitz Algebras and Extensions of\\Irrational Rotation Algebras
For a given irrational number $\theta$, we define Toeplitz operators with symbols in the irrational rotation algebra ${\mathcal A}_\theta$, and we show that the $C^*$-algebra $\mathcal T({\mathcal A}_\theta)$ generated by these Toeplitz operators is an extension of ${\mathcal A}_\theta$ by the algebra of compact operators. We then use these extensions to explicitly exhibit generators of the group $KK^1({\mathcal A}_\theta,\mathbb C)$. We also prove an index theorem for $\mathcal T({\mathcal A}_\theta)$ that generalizes the standard index theorem for Toeplitz operators on the circle.

Keywords:Toeplitz operators, irrational rotation algebras, index theory
Categories:47B35, 46L80

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