Composition Operators with Monomial Symbol Acting on Weighted Hardy Spaces

Let C φ be the composition operator with monomial symbol φ ( z ) = z m , z ∈ D , for some positive integer m . In this article, we investigate the point spectrum, spectrum, and essential spectrum of the operators C φ ∗ C φ , C φ C φ ∗ , self-commutator [ C φ ∗ , C φ ] and anti-self-commutator { C φ...

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Bibliographic Details
Published in:Mediterranean journal of mathematics 2018-02, Vol.15 (1), p.1-14, Article 2
Main Authors: Heller, Katherine C., Pons, Matthew A.
Format: Article
Language:English
Subjects:
Dirichlet problem
Mathematics
Mathematics and Statistics
Operators
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Summary:Let C φ be the composition operator with monomial symbol φ ( z ) = z m , z ∈ D , for some positive integer m . In this article, we investigate the point spectrum, spectrum, and essential spectrum of the operators C φ ∗ C φ , C φ C φ ∗ , self-commutator [ C φ ∗ , C φ ] and anti-self-commutator { C φ ∗ , C φ } on weighted Hardy spaces H 2 ( β ) and recover known results for the classical Hardy, Bergman, and Dirichlet spaces.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-017-1040-5