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arXiv · 0707.3425

Norms and spectral radii of linear fractional composition operators on the ball

Michael T. Jury
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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 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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Michael T. Jury. 2007-07-23. Norms and spectral radii of linear fractional composition operators on the ball. https://arxiv.org/abs/0707.3425

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