Journal of Operator Theory

Volume 58, Issue 1, Summer 2007 pp. 135-156.

Toeplitz-composition $C^*$-algebras

Authors: Thomas L. Kriete (1), Barbara D. MacCluer (2), and Jennifer L. Moorhouse (3)
Author institution: (1) Department of Mathematics, University of Virginia, P.O. Box 400137, Charlottesville, VA 22904, USA
(2) Department of Mathematics, University of Virginia, P.O. Box 400137, Charlottesville, VA 22904, USA
(3) Department of Mathematics, Colgate University, Hamilton, NY 13356, USA

Summary: Let $\zeta$ and $\eta$ be distinct points on the unit circle and suppose that $\varphi$ is a linear-fractional self-map of the unit disk $\D$, not an automorphism, with $\varphi(\zeta)=\eta$. We describe the $C^*$-algebra generated by the associated composition operator $\cp$ and the shift operator, acting on the Hardy space on $\D$.

Keywords: Composition operator, Toeplitz operator, $C^*$-algebra

Contents Full-Text PDF