Quasi-parabolic Composition Operators on Weighted Bergman Spaces
COMPLEX ANALYSIS AND OPERATOR THEORY, vol.12, no.1, pp.55-79, 2018 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 12 Issue: 1
- Publication Date: 2018
- Doi Number: 10.1007/s11785-016-0577-9
- Journal Name: COMPLEX ANALYSIS AND OPERATOR THEORY
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.55-79
- Open Archive Collection: AVESIS Open Access Collection
- Hacettepe University Affiliated: Yes
Abstract
In this work we study the essential spectra of composition operators on weighted Bergman spaces of analytic functions which might be termed as "quasi-parabolic." This is the class of composition operators on with symbols whose conjugate with the Cayley transform on the upper half-plane are of the form , where and . We especially examine the case where is discontinuous at infinity. A similar method used in Gul (J Math Anal Appl 377:771-791, 2011) for Hardy spaces is used 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.