Erratum to: The algebraic structure of non-commutative analytic Toeplitz algebras

Authors

Kenneth R. Davidson, Pure Math. Dept., U. Waterloo
David R. Pitts, University of Nebraska-LincolnFollow

Document Type

Article

Date of this Version

2015

Citation

Math. Ann. (2015) 361:1123–1124

Comments

© Springer-Verlag Berlin Heidelberg 2015

Abstract

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 B_n,k of R_n(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 π⁻¹ 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 π⁻¹ ∞,1(0) is very large—it contains a copy of the βN\N.