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Search: All articles in the CMB digital archive with keyword Toeplitz operator

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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

2. CMB 1998 (vol 41 pp. 196)

Nakazi, Takahiko
Brown-Halmos type theorems of weighted Toeplitz operators
The spectra of the Toeplitz operators on the weighted Hardy space $H^2(Wd\th/2\pi)$ and the Hardy space $H^p(d\th/2\pi)$, and the singular integral operators on the Lebesgue space $L^2(d\th/2\pi)$ are studied. For example, the theorems of Brown-Halmos type and Hartman-Wintner type are studied.

Keywords:Toeplitz operator, singular integral, operator, weighted Hardy space, spectrum.
Category:47B35

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