Essential spectra of quasi-parabolic composition operators on Hardy spaces of analytic functions


Gul U.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, cilt.377, ss.771-791, 2011 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 377 Konu: 2
  • Basım Tarihi: 2011
  • Doi Numarası: 10.1016/j.jmaa.2010.11.055
  • Dergi Adı: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Sayfa Sayıları: ss.771-791

Özet

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 epsilon H(infinity)(H) and (sic)(psi(z)) > epsilon > 0. We especially examine the case where psi is discontinuous at infinity. A new method is devised to show that this type of composition operator 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. (c) 2010 Elsevier Inc. All rights reserved.