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

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.

arXiv comment25 pages

Cited by in corpus (4)

• Essential Spectra of Quasi-parabolic Composition Operators on Hardy Spaces of the Poly-disc
• Quasi-parabolic Composition Operators on Weighted Bergman Spaces
• On the C*-algebra Generated by Toeplitz Operators and Fourier Multipliers on the Hardy Space of a Locally Compact Group
• Parabolic Non-Automorphism Induced Toeplitz-Composition C*-Algebras with Piece-wise Quasi-continuous Symbols