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Spring 2018 The compactness of a class of radial operators on weighted Bergman spaces
Yucheng Li, Maofa Wang, Wenhua Lan
Adv. Oper. Theory 3(2): 400-410 (Spring 2018). DOI: 10.15352/AOT.1707-1202

Abstract

In this paper, we study some connection between the compactness of radial operators and the boundary behavior of the corresponding Berezin transform on weighted Bergman spaces. More precisely, we prove that, under some mild condition, the vanishing of the Berezin transform on the unit circle is equivalent to the compactness of a class of radial operators on weighted Bergman spaces. Moreover, we also study the radial essential commutant of the Toeplitz operator $T_z$.

Citation

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Yucheng Li. Maofa Wang. Wenhua Lan. "The compactness of a class of radial operators on weighted Bergman spaces." Adv. Oper. Theory 3 (2) 400 - 410, Spring 2018. https://doi.org/10.15352/AOT.1707-1202

Information

Received: 21 June 2017; Accepted: 26 October 2017; Published: Spring 2018
First available in Project Euclid: 15 December 2017

zbMATH: 06848508
MathSciNet: MR3738220
Digital Object Identifier: 10.15352/AOT.1707-1202

Subjects:
Primary: 47B35
Secondary: ‎32A36‎

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.3 • No. 2 • Spring 2018
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