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The objective of this paper is to study wandering subspaces for commutingtuples of bounded operators on Hilbert spaces. It is shown that, for a largeclass of analytic functional Hilbert spaces $\mathcal{H}_K$ 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$\mathcal{H}_K$-inner functions. We prove that $\mathcal{H}_K$-inner functionsare contractive multipliers and deduce a result on the multiplier norm ofquasi-homogenous polynomials as an application. Along the way we prove arefinement of a result of Arveson on the uniqueness of minimal dilations ofpure row contractions.

Dilations, Wandering Subspaces, and Inner Functions