Characteristic functions for multicontractions and automorphisms of the unit ball

TL;DR

This paper studies the characteristic functions of multicontractions on Hilbert spaces and examines how these functions behave under automorphisms of the unit ball, contributing to operator theory and complex analysis.

Contribution

It introduces new results on the behavior of characteristic functions of multicontractions under automorphisms of the unit ball.

Findings

Characteristic functions of multicontractions are analyzed.

Behavior under automorphisms of the unit ball is characterized.

Results connect operator theory with complex automorphism groups.

Abstract

A \emph{multicontraction} on a Hilbert space $\HH$ is an $n$-tuple of operators $T=(T_1,...,T_n)$ acting on $\HH$, such that $\sum_{i=1}^n T_i T_i^*\le \1_\HH$. 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.