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On C*-Algebras of Toeplitz Operators on the Harmonic Bergman Space

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Abstract

Commutative algebras of Toeplitz operators acting on the Bergman space on the unit disk have been completely classified in terms of geometric properties of the symbol class. The question when two Toeplitz operators acting on the harmonic Bergman space commute is still open. In some papers, conditions on the symbols have been given in order to have commutativity of two Toeplitz operators. In this paper, we describe three different algebras of Toeplitz operators acting on the harmonic Bergman space: The C*-algebra generated by Toeplitz operators with radial symbols, in the elliptic case; the C*-algebra generated by Toeplitz operators with piecewise continuous symbols, in the parabolic and hyperbolic cases. We prove that the Calkin algebra of the first two algebras are commutative, like in the case of the Bergman space, while the last one is not.

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Authors and Affiliations

  1. Departamento de Matemáticas, CINVESTAV del I.P.N., Apartado Postal 14-740, 07000, México, D.F, México

    Maribel Loaiza & Carmen Lozano

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  1. Maribel Loaiza
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  2. Carmen Lozano
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Correspondence to Maribel Loaiza.

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This work was partially supported by CONACYT Project 102800.

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Loaiza, M., Lozano, C. On C*-Algebras of Toeplitz Operators on the Harmonic Bergman Space. Integr. Equ. Oper. Theory 76, 105–130 (2013). https://doi.org/10.1007/s00020-013-2046-4

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  • DOI: https://doi.org/10.1007/s00020-013-2046-4

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