Characteristic Functions for Multicontractions and Automorphisms of the Unit Ball

Abstract.

A multicontraction on a Hilbert space $\user1{\mathcal{H}}$ is an n-tuple of operators T = (T₁,..., T _n ) acting on $\user1{\mathcal{H}}$, such that $\sum\nolimits_{i = 1}^n {T_i T_i^* \, \leq \,1_\user1{\mathcal{H}}}$. We obtain some results related to the characteristic function of a commuting multicontraction, most notably discussing its behaviour with respect to the action of the analytic automorphisms of the unit ball.