Erratum to: Automorphisms and Dilation Theory of Triangular UHF Algebras

Abstract

It has come to the author’s attention that Proposition 3.3 in the original article is false. This proposition stated that every triangular UHF algebra is isometrically isomorphic to a triangular UHF algebra with regular embeddings. See Power’s book [1] or [2]. Recall that a unital embedding φ : Tkn → Tkn+1 is called regular when it preserves the normalizer: φ(NCn(Tkn) ⊂ NCn+1(Tkn+1),where NCn(Tkn) = {v ∈ Tknpartial isometry : vCnv∗ ⊂ Cn, v∗Cnv ⊂ Cn}. The assumption that the embeddings are regular was mistakenly absent from the hypotheses for the definition of the topological binary relation (cf. [1]), and this concept was the main tool in the incorrect proof. However, by simply replacing the use of Proposition 3.3 at the beginning of every proof in the remainder of the paper and adding the hypothesis that we are dealing with algebras with regular embeddings the rest of the paper is correct. Note that one needs no regularity assumption in Sect. 6, Dilation theory.