Functional models for $\hat{I}{“}_n$-contractions

Abstract

This article develops several functional models for a given $\hat{I}{“}_n$-contraction. The first model is motivated by the Douglas functional model for a contraction. We then establish factorization results that clarify the relationship between a minimal isometric dilation and an arbitrary isometric dilation of a contraction. Using these factorization results, we obtain a Sz.-Nagy-Foias type functional model for a completely non-unitary $\hat{I}{“}_n$-contraction, as well as Schäffer type functional model for $\hat{I}{“}_n$-contraction.

This is the initial version. Final version will be submitted soon