Kenneth R. Davidson - Nevanlinna-Pick interpolation for non-commutative analytic Toeplitz algebras

The non-commutative analytic Toeplitz algebra is the -closed algebra generated by the left regular representation of the free semigroup on n generators. We obtain a distance formula to an arbitrary -closed right ideal and thereby show that the quotient is completely isometrically isomorphic to the compression of the algebra to the orthogonal complement of the range of the ideal. This is used to obtain Nevanlinna-Pick type interpolation theorems.