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Integral Equations and Operator Theory

, Volume 83, Issue 1, pp 49–60 | Cite as

Radial Toeplitz Operators Revisited: Discretization of the Vertical Case

  • Crispin Herrera Yañez
  • Nikolai Vasilevski
  • Egor A. Maximenko
Article

Abstract

It is known that radial Toeplitz operators acting on a weighted Bergman space of the analytic functions on the unit ball generate a commutative C*-algebra. This algebra has been explicitly described via its identification with the C*-algebra \({{\rm VSO}(\mathbb{N})}\) of bounded very slowly oscillating sequences (these sequences was used by R. Schmidt and other authors in Tauberian theory). On the other hand, it was recently proved that the C*-algebra generated by Toeplitz operators with bounded measurable vertical symbols is unitarily isomorphic to the C*-algebra \({{\rm VSO}(\mathbb{R}_+)}\) of “very slowly oscillating functions”, i.e. the bounded functions that are uniformly continuous with respect to the logarithmic distance \({\rho(x,y)=|\ln(x)-\ln(y)|}\). In this note we show that the results for the radial case can be easily deduced from the results for the vertical one.

Keywords

Bergman space Toeplitz operators radial symbols very slowly oscillating functions 

Mathematics Subject Classification

Primary 47B35 Secondary 32A36 44A35 44A15 

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  • Crispin Herrera Yañez
    • 1
  • Nikolai Vasilevski
    • 1
  • Egor A. Maximenko
    • 2
  1. 1.Departamento de MatemáticasCINVESTAVMexicoMexico
  2. 2.Escuela Superior de Física y MatemáticasInstituto Politécnico NacionalMexicoMexico

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