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arXiv · 1002.4640

Essential Spectra of Quasi-parabolic Composition Operators on Hardy Spaces of Analytic Functions

Ugur Gul
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Abstract

In this work we study the essential spectra of composition operators on Hardy spaces of analytic functions which might be termed as "quasi-parabolic". This is the class of composition operators on H^{2} with symbols whose conjugate with the Cayley transform on the upper half-plane are of the form ϕ(z) = z+ψ(z) where ψ\in H^{2}(\mathbb{H}) and \Im(ψ(z)) >δ> 0. We especially examine the case where ψis discontinuous at infinity. A new method is devised to show that this type of composition operators fall in a C*-algebra of Toeplitz operators and Fourier multipliers. This method enables us to provide new examples of essentially normal composition operators and to calculate their essential spectra.

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BibTeXRIS

Ugur Gul. 2010-11-09. Essential Spectra of Quasi-parabolic Composition Operators on Hardy Spaces of Analytic Functions. https://doi.org/10.1016/j.jmaa.2010.11.055

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