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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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

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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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

weighted Bergman space radial operator Berezin transform compact operator essential commutant


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.

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