# Dilations, Wandering subspaces, and inner functions

#### Description

The objective of this work is to study wandering subspaces for commuting tuples of bounded operators on Hilbert spaces. It is shown that, for a large class of analytic functional Hilbert spaces on the unit ball in $\mathbb C^n$, wandering subspaces for restrictions of the multiplication tuple $M_z = (M_{z_1}, \ldots ,M_{z_n})$ can be described in terms of suitable inner multipliers. Necessary and sufficient conditions for the wandering subspaces to be generating are given. Along the way we prove a useful uniqueness result for minimal dilations of pure row contractions.

*This paper has been withdrawn.*

Dilations, Wandering subspaces, and inner functions

Cupples I Room 207

The objective of this work is to study wandering subspaces for commuting tuples of bounded operators on Hilbert spaces. It is shown that, for a large class of analytic functional Hilbert spaces on the unit ball in $\mathbb C^n$, wandering subspaces for restrictions of the multiplication tuple $M_z = (M_{z_1}, \ldots ,M_{z_n})$ can be described in terms of suitable inner multipliers. Necessary and sufficient conditions for the wandering subspaces to be generating are given. Along the way we prove a useful uniqueness result for minimal dilations of pure row contractions.