## Functiones et Approximatio Commentarii Mathematici

### On compactness of Toeplitz operators in Bergman spaces

#### Abstract

In this paper we consider Toepliz operators with (locally) integrable symbols acting on Bergman spaces $A^p$ ($1<p<\infty$) of the open unit disc of the complex plane. We give a characterization of compact Toeplitz operators with symbols in $L^1$ under a mild additional condition. Our result is new even in the Hilbert space setting of $A^2$, where it extends the well-known characterization of compact Toeplitz operators with bounded symbols by Stroethoff and Zheng.

#### Article information

Source
Funct. Approx. Comment. Math., Volume 59, Number 2 (2018), 305-318.

Dates
First available in Project Euclid: 18 December 2018

https://projecteuclid.org/euclid.facm/1545102410

Digital Object Identifier
doi:10.7169/facm/1727

Mathematical Reviews number (MathSciNet)
MR3892308

Zentralblatt MATH identifier
07055558

#### Citation

Taskinen, Jari; Virtanen, Jani. On compactness of Toeplitz operators in Bergman spaces. Funct. Approx. Comment. Math. 59 (2018), no. 2, 305--318. doi:10.7169/facm/1727. https://projecteuclid.org/euclid.facm/1545102410

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