Journal of Operator Theory

Volume 67, Issue 2, Spring 2012 pp. 537-560.

Spectra of some composition operators and associated weighted composition operators

Authors: Paul S. Bourdon
Author institution: Mathematics Department, Washington and Lee University, Lexington, VA 24450, U.S.A.

Summary: We characterize the spectrum and essential spectrum of "essentially linear fractional" composition operators acting upon the Hardy space

$H^2(\U)$ of the open unit disc

$\U$ . When the symbols of these composition operators have Denjoy--Wolff point on the unit circle, the spectrum and essential spectrum coincide. Our work permits us to describe the spectrum and essential spectrum of certain associated weighted composition operators on

$H^2(\U)$ .

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