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

#### 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
Accepted: 26 October 2017
First available in Project Euclid: 15 December 2017

https://projecteuclid.org/euclid.aot/1513328639

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

#### 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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