Radial Toeplitz Operators Revisited: Discretization of the Vertical Case

Crispin Herrera Yañez, Nikolai Vasilevski, Egor A. Maximenko

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6 Scopus citations

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 VSO(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 VSO(R+) of “very slowly oscillating functions”, i.e. the bounded functions that are uniformly continuous with respect to the logarithmic distance ρ(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.

Original languageEnglish
Pages (from-to)49-60
Number of pages12
JournalIntegral Equations and Operator Theory
Volume83
Issue number1
DOIs
StatePublished - 23 Sep 2015

Keywords

  • Bergman space
  • Toeplitz operators
  • radial symbols
  • very slowly oscillating functions

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