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On Toeplitz operators on the pluriharmonic Bergman space on the Siegel domain

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Abstract

We prove that Toeplitz operators, acting on the pluriharmonic Bergman space of the Siegel domain, generate commutative \(C^*\)- algebras in the following two cases: when the class of symbols are invariant functions under the action of the quasi-parabolic group of biholomorphisms of the Siegel domain and when the class of symbols consists of all invariant functions under the action of the nilpotent group of biholomorphisms of the Siegel domain.

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Authors and Affiliations

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

    Maribel Loaiza

  2. Instituto de Matemáticas, Unidad Cuernavaca, Universidad Nacional Autónoma de México, A.P. 273-3, ADMON 3, 62251, Cuernavaca, Mor, Mexico

    Carmen Lozano

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

Additional information

To S. M. Grudsky on the occasion of his 60th birthday.

This work was partially supported by CONACYT project 238630 and by the Grant PAPIIT-UNAM IN/02915.

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Loaiza, M., Lozano, C. On Toeplitz operators on the pluriharmonic Bergman space on the Siegel domain. Bol. Soc. Mat. Mex. 22, 583–604 (2016). https://doi.org/10.1007/s40590-016-0122-x

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  • DOI: https://doi.org/10.1007/s40590-016-0122-x

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