Factoring in non-commutative analytic Toeplitz algebras

The Iron-commutative analytic Toeplitz algebra is the WOT-closed algebra generated by the left regular representation of the free semigroup on n generators. The structure theory of contractions in these algebras is examined. Each is shown to have an HCC functional calculus. The isometries defined by words are shown to factor only as the words do over the unit ball of the algebra. This turns out to be false over the full algebra. The natural identification of WOT-closed left ideals with invariant subspaces of the algebra is shown to hold only for a proper subcollection of the subspaces.