Advances in Operator Theory
- Adv. Oper. Theory
- Volume 3, Number 2 (2018), 400-410.
The compactness of a class of radial operators on weighted Bergman spaces
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 $T_z$.
Adv. Oper. Theory, Volume 3, Number 2 (2018), 400-410.
Received: 21 June 2017
Accepted: 26 October 2017
First available in Project Euclid: 15 December 2017
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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