JournalsrmiVol. 29, No. 3pp. 789–808

An operator inequality for weighted Bergman shift operators

  • Anders Olofsson

    Lund University, Sweden
  • Aron Wennman

    Royal Institute of Technology, Stockholm, Sweden
An operator inequality for weighted   Bergman shift operators cover

Abstract

We prove an operator inequality for the Bergman shift operator on weighted Bergman spaces of analytic functions in the unit disc with weight function controlled by a curvature parameter α\alpha assuming nonnegative integer values. This generalizes results by Shimorin, Hedenmalm and Jakobsson concerning the cases α=0\alpha=0 and α=1\alpha=1. A naturally derived scale of Hilbert space operator inequalities is studied and shown to be relaxing as the parameter α>1\alpha>-1 increases. Additional examples are provided in the form of weighted shift operators.

Cite this article

Anders Olofsson, Aron Wennman, An operator inequality for weighted Bergman shift operators. Rev. Mat. Iberoam. 29 (2013), no. 3, pp. 789–808

DOI 10.4171/RMI/740