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Revista Matemática Iberoamericana

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Volume 29, Issue 3, 2013, pp. 789–808
DOI: 10.4171/RMI/740

Published online: 2013-08-04

An operator inequality for weighted Bergman shift operators

Anders Olofsson[1] and Aron Wennman[2]

(1) Lund University, Sweden
(2) Royal Institute of Technology, Stockholm, Sweden

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 $\alpha$ assuming nonnegative integer values. This generalizes results by Shimorin, Hedenmalm and Jakobsson concerning the cases $\alpha=0$ and $\alpha=1$. A naturally derived scale of Hilbert space operator inequalities is studied and shown to be relaxing as the parameter $\alpha>-1$ increases. Additional examples are provided in the form of weighted shift operators.

Keywords: Bergman shift operator, operator inequality, weighted shift operator

Olofsson Anders, Wennman Aron: An operator inequality for weighted Bergman shift operators. Rev. Mat. Iberoam. 29 (2013), 789-808. doi: 10.4171/RMI/740