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 $H^2(\U)$.

Keywords: composition operator, weighted composition operator, Hardy space, spectrum, essential spectrum, compression spectrum

Contents Full-Text PDF