Journal of Operator Theory
Volume 58, Issue 1, Summer 2007 pp. 135-156.
Toeplitz-composition $C^*$-algebrasAuthors: 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 $\D$.
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