Mathematics, Department of


Date of this Version



Math. Ann. (2015) 361:1123–1124


© Springer-Verlag Berlin Heidelberg 2015


The algebraic structure of the non-commutative analytic Toeplitz algebra Ln is developed in the original article. Some of the results fail for the case n = ∞, and this implies that certain other results are not established in this case. In Theorem 3.2 of the original article, we showed there is continuous surjection πn,k from Repk (Ln), the space of completely contractive representations of Ln into the k × k matrices Mk , onto the closed unit ball Bn,k of Rn(Mk ) by evaluation at the generators. It is further claimed that if T = [T1, . . . , Tn] ∈ Rn(Mk ) with T < 1, then there is a unique representation in π1 n,k (T ). Further information is obtained for k = 1 in Theorem 3.3 of the original article. Our proof of these results is valid for n < ∞, however, for n = ∞ the uniqueness claim is incorrect. An example due to Michael Hartz (see [2, Example 2.4]) shows that π1,1(0) is very large—it contains a copy of the βN\N.