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JOURNALS // Trudy Matematicheskogo Instituta imeni V.A. Steklova // Archive
Trudy Mat. Inst. Steklova, 2020 Volume 311, Pages 241–249 (Mi tm4118)
Trace Class Toeplitz Operators with Singular Symbols

Grigori V. Rozenblumab, Nikolai L. Vasilevskic

a Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, SE-412 96 Gothenburg, Sweden
b Faculty of Physics, St. Petersburg State University, Petergof, Ul'yanovskaya ul. 1, St. Petersburg, 198504 Russia
c Departamento de Matemáticas, Cinvestav, Av. Instituto Politécnico Nacional 2508, Col. San Pedro Zacatenco, Ciudad de México, CP 07360, Mexico

Abstract: We provide sufficient conditions for Toeplitz operators with distributional symbols acting on the Bergman space on the unit disk to be trace class. The Berezin transform of distributions, introduced in the paper, yields a formula for the trace. Several instructive examples are also given.

Keywords: Bergman space, Toeplitz operators, distributional symbol.

UDC: 517.983.26

MSC: 47A75 (primary), 58J50 (secondary)

Received: February 16, 2020
Revised: April 7, 2020
Accepted: June 24, 2020

DOI: 10.4213/tm4118


 English version: Proceedings of the Steklov Institute of Mathematics, 2020, 311, 225–232

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© Steklov Math. Inst. of RAS, 2024