Necessary condition for compactness of a difference of composition operators on the Dirichlet space

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:426

Article

Michalska, Malgorzata¹  Michalski, Andrzej M.² 

[1] Marie Curie Sklodowska Univ, Inst Math, PL-20031 Lublin, Poland

[2] John Paul II Catholic Univ Lublin, Dept Complex Anal, PL-20950 Lublin, Poland

关键词: Composition operator;    Dirichlet space;    Compact operator;    Commutator;   

DOI  :  10.1016/j.jmaa.2015.02.002

来源: Elsevier

【 摘 要 】

Let phi be a self-map of the unit disk and let C-phi denote the composition operator acting on the standard Dirichlet space D. A necessary condition for compactness of a difference of two bounded composition operators acting on D is given. As an application, a characterization of disk automorphisms phi and psi, for which the commutator [C-psi*, C phi] is compact, is given. (C) 2015 Published by Elsevier Inc.

【 授权许可】

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