2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/134861We 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.15 pagesFunctional Analysis47B33 (primary), 32A17 (secondary)text