Mathematics – Functional Analysis
Scientific paper
2010-02-24
Mathematics
Functional Analysis
25 pages
Scientific paper
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 \phi(z) = z+\psi(z) where \psi\in H^{2}(\mathbb{H}) and \Im(\psi(z)) >\delta > 0. We especially examine the case where \psi is 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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