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Integral Equations and Operator Theory

, Volume 83, Issue 3, pp 413–428 | Cite as

C*-Algebra Generated by Angular Toeplitz Operators on the Weighted Bergman Spaces Over the Upper Half-Plane

  • Kevin Esmeral
  • Egor A. Maximenko
  • Nikolai Vasilevski
Article

Abstract

We consider the set of all Toeplitz operators acting on the weighted Bergman space over the upper half-plane whose L -symbols depend only on the argument of the polar coordinates. The main result states that the uniform closure of this set coincides with the C*-algebra generated by the above Toeplitz operators and is isometrically isomorphic to the C*-algebra of bounded functions that are very slowly oscillating on the real line in the sense that they are uniformly continuous with respect to the arcsinh-metric on the real line.

Mathematics Subject Classification

Primary: 47B35 Secondary: 32A36 

Keywords

Bergman space Toeplitz operators angular symbols very slowly oscillating functions 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  • Kevin Esmeral
    • 1
  • Egor A. Maximenko
    • 2
  • Nikolai Vasilevski
    • 1
  1. 1.Department of MathematicsCINVESTAV-IPNMexicoMexico
  2. 2.Escuela Superior de Física y MatemáticasInstituto Politécnico NacionalMexicoMexico

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