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

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

2007-07-23

arxiv.org/abs/0707.3425v1

Mathematics

Functional Analysis

15 pages

Scientific paper

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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