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December 2018 On compactness of Toeplitz operators in Bergman spaces
Jari Taskinen, Jani Virtanen
Funct. Approx. Comment. Math. 59(2): 305-318 (December 2018). DOI: 10.7169/facm/1727

Abstract

In this paper we consider Toepliz operators with (locally) integrable symbols acting on Bergman spaces $A^p$ ($1<p<\infty$) of the open unit disc of the complex plane. We give a characterization of compact Toeplitz operators with symbols in $L^1$ under a mild additional condition. Our result is new even in the Hilbert space setting of $A^2$, where it extends the well-known characterization of compact Toeplitz operators with bounded symbols by Stroethoff and Zheng.

Citation

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Jari Taskinen. Jani Virtanen. "On compactness of Toeplitz operators in Bergman spaces." Funct. Approx. Comment. Math. 59 (2) 305 - 318, December 2018. https://doi.org/10.7169/facm/1727

Information

Published: December 2018
First available in Project Euclid: 18 December 2018

zbMATH: 07055558
MathSciNet: MR3892308
Digital Object Identifier: 10.7169/facm/1727

Subjects:
Primary: 47B35

Rights: Copyright © 2018 Adam Mickiewicz University

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Vol.59 • No. 2 • December 2018
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