696 research outputs found
Norms and spectral radii of linear fractional composition operators on the ball
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.Comment: 15 page
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