Journal of Mathematical Physics, Analysis, Geometry
2020, vol. 16, No 1, pp. 3-26   https://doi.org/10.15407/mag16.01.003     ( to contents , go back )
https://doi.org/10.15407/mag16.01.003

Toeplitz Operators with Radial Symbols on Bergman Space and Schatten-von Neumann Classes

Z. Bendaoud

Faculté des Sciences, Université Amar Telidji-Laghouat, B.P. 37G, route de Ghardaia, Laghouat 03000, Algérie
E-mail: zbendaoud@gmail.com

S. Kupin

Institut de Mathématiques de Bordeaux UMR5251, CNRS, Université de Bordeaux, 351 ave. de la Libération, 33405 Talence Cedex, France
E-mail: skupin@math.u-bordeaux.fr

K. Toumache

Faculté des Sciences Exactes, des Sciences de la Nature et de la Vie, Université Mohamed Khider-Biskra, B.P. 145, Biskra 07000, Algérie
E-mail: kamel toumache@yahoo.fr

B. Touré

Faculté des Sciences et des Techniques, Université des Sciences, des Techniques et des Technologies de Bamako, Campus Universitaire de Badalabougou à Bamako, B.P. E-3206, Bamako, Mali
E-mail: vbelco@yahoo.fr

R. Zarouf

Institut de Mathématiques de Marseille, UMR 7373, Aix-Marseille Université, 39 rue F. Joliot Curie, 13453 Marseille Cedex 13, France
E-mail: rzarouf@gmail.com

Received December 12, 2018, revised April 8, 2019.

Abstract

In the present paper, we study spectral properties of Toeplitz operators with (quasi-) radial symbols on Bergman space. More precisely, the problem we are interested in is to understand when a given Toeplitz operator belongs to a Schatten-von Neumann class. The methods of the approximation theory (i.e., Legendre polynomials) are used to advance in this direction.

Mathematics Subject Classification 2000: 47B35, 30H20, 42C10.
Key words: Toeplitz operators, (quasi-) radial symbols, Bergman spaces, Schatten - von Neumann classes, Legendre polynomials.

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