Characteristic Functions for Ergodic Tuples

Abstract

Motivated by a result on weak Markov dilations, we define a notion of characteristic function for ergodic and coisometric row contractions with a one-dimensional invariant subspace for the adjoints. This extends a definition given by G. Popescu. We prove that our characteristic function is a complete unitary invariant for such tuples and show how it can be computed.

22 pages, changes made after referee's comments, to appear in Integral Equations and Operator Theory