Commutative Algebras of Toeplitz Operators on the Bergman Space Revisited: Spectral Theorem Approach
Journal article, 2022

For three standard models of commutative algebras generated by Toeplitz operators in the weighted analytic Bergman space on the unit disk, we find their representations as the algebras of bounded functions of certain unbounded self-adjoint operators. We discuss main properties of these representation and, especially, describe relations between properties of the spectral function of Toeplitz operators in the spectral representation and properties of the symbols.

Commutative algebras

Toeplitz operators

Spectral representation


Grigori Rozenblioum

Sirius University of Science and Technology

Euler International Mathematical Institute

Chalmers, Mathematical Sciences

N. Vasilevski

Centro de Investigacion y de Estudios Avanzados Centro de Investigacion y de Estudios Avanzados (CINVESTAV)

Integral Equations and Operator Theory

0378-620X (ISSN) 1420-8989 (eISSN)

Vol. 94 3 27

Subject Categories

Algebra and Logic


Mathematical Analysis



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