Journal of Operator Theory

Volume 39, Issue 2, Spring 1998 pp. 283-296.

A note on the spectra of certain composition operators on Hardy spaces

Authors: Georg Hoever
Author institution: Mathematisches Institut, Universitaet Muenchen, Theresienstr. 39, 80333 Muenchen, Germany

Summary: H.\ Kamowitz claimed that the spectra of certain composition operators on Hardy spaces, induced by analytic selfmappings $\varphi$ of the open unit disk, which have Denjoy-Wolff point of modulus one with angular derivative less than one, are discs. C.C.\ Cowen discovered a gap in the proof and gave a new suggestion, applying different methods for different areas of points asserted to lie in the spectrum. In one of these he uses a continuity assertion of his `model of iteration', which seems not to be proved completly. This paper fills the gap in Kamowitz's proof precisely in this case and gives little generalizations.

Keywords: Composition operator, spectrum

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