Skip to main content

Commutative C*-Algebras of Toeplitz Operators on the Unit Ball, I. Bargmann-Type Transforms and Spectral Representations of Toeplitz Operators

Integral Equations and Operator Theory volume 59, pages 379–419 (2007)Cite this article

Abstract.

Extending known results for the unit disk, we prove that for the unit ball \({\mathbb{B}}^n\) there exist n+2 different cases of commutative C*-algebras generated by Toeplitz operators, acting on weighted Bergman spaces. In all cases the bounded measurable symbols of Toeplitz operators are invariant under the action of certain commutative subgroups of biholomorphisms of the unit ball.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

39,95 €

Price includes VAT (Finland)

Author information

Authors and Affiliations

  1. Centro de Investigación en Matemáticas, Apartado Postal 402, 36000, Guanajuato, Gto., México

    Raul Quiroga-Barranco

  2. Departamento de Matemáticas, CINVESTAV, Apartado Postal 14-740, 07000, México, D.F., México

    Nikolai Vasilevski

Authors
  1. Raul Quiroga-Barranco
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nikolai Vasilevski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nikolai Vasilevski.

Additional information

This work was partially supported by CONACYT Projects 46936 and 44620, México.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Quiroga-Barranco, R., Vasilevski, N. Commutative C*-Algebras of Toeplitz Operators on the Unit Ball, I. Bargmann-Type Transforms and Spectral Representations of Toeplitz Operators. Integr. equ. oper. theory 59, 379–419 (2007). https://doi.org/10.1007/s00020-007-1537-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00020-007-1537-6

Mathematics Subject Classification (2000).

  • Primary 47B35
  • Secondary 47L80, 32A36

Keywords.

  • Toeplitz operator
  • Bergman space
  • commutative C*-algebra
  • unit ball
  • commutative groups of biholomorphisms