Norms and spectral radii of linear fractional composition operators on the ball |
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Authors: | Michael T Jury |
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Institution: | Department of Mathematics, University of Florida, Gainesville, FL 32603, USA |
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Abstract: | We give a new proof that every linear fractional map of the unit ball induces a bounded composition operator on the standard scale of Hilbert function spaces on the ball, and obtain new norm bounds analogous to the standard one-variable estimates. We also show that Cowen's one-variable spectral radius formula extends to these operators. The key observation underlying these results is that every linear fractional map of the ball belongs to the Schur-Agler class. |
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Keywords: | Composition operator Schur-Agler class Linear fractional map Norm Spectral radius |
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