An operator inequality for weighted Bergman shift operators
Copyright policy )An operator inequality for weighted Bergman shift operators
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.
- Royal Institute of Technology Sweden
- Lund University Sweden
Bergman spaces and Fock spaces, shift operator, Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces), weighted Bergman spaces, Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces), log-subharmonic weights, operator inequality
Bergman spaces and Fock spaces, shift operator, Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces), weighted Bergman spaces, Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces), log-subharmonic weights, operator inequality
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