Advances in Operator Theory

The compactness of a class of radial operators on weighted Bergman spaces

Yucheng Li, Maofa Wang, and Wenhua Lan

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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 $T_z$.

Article information

Source
Adv. Oper. Theory Volume 3, Number 2 (2018), 400-410.

Dates
Received: 21 June 2017
Accepted: 26 October 2017
First available in Project Euclid: 15 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.aot/1513328639

Digital Object Identifier
doi:10.15352/AOT.1707-1202

Subjects
Primary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]
Secondary: 32A36: Bergman spaces

Keywords
weighted Bergman space radial operator Berezin transform compact operator essential commutant

Citation

Li, Yucheng; Wang, Maofa; Lan, Wenhua. The compactness of a class of radial operators on weighted Bergman spaces. Adv. Oper. Theory 3 (2018), no. 2, 400--410. doi:10.15352/AOT.1707-1202. https://projecteuclid.org/euclid.aot/1513328639


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