Revista Matemática Iberoamericana
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Published online: 2013-08-04
An operator inequality for weighted Bergman shift operatorsAnders Olofsson and Aron Wennman (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