Compactness of composition operators on the Bergman space of the bidisc

2024/09/14 by Timothy G. Clos, Clos, Timothy G., Željko Čučković +3
Mathematics · #32A36 #47B33 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2409.09529

openalex publication_date 2024/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let φ be a holomorphic self map of the bidisc that is Lipschitz on the closure. We show that the composition operator C_φ is compact on the Bergman space if and only if φ(\mathbbD²)∩ \mathbbT²=∅ and φ(\mathbbD²∖ \mathbbT²)∩ b\mathbbD²=∅.

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