Erratum to: Inverse-Closed Algebras of Integral Operators on Locally Compact Groups

Abstract

It was pointed out by Detlev Poguntke that the values of the map θ in the proof of Proposition 2.7 of original article may not be equivalence classes of Bochner integrable functions. Consequently the statements of Proposition 2.7, Corollary 2.8, Theorem 3.10, Theorem 5.2, and Corollary 5.3 of original article are not correct, and an extra hypothesis is needed in these statements in order to obtain the corresponding conclusions. Details in this connection can be found below. One of the situations when the proof of Proposition 2.7 of original article applies is that of discrete groups, so that hypothesis will be added in the statement as follows. Proposition 0.1. Let G be a discrete group and (A, G, α) be a C∗-dynamical system. Then there exists a C∗-dynamical system (Ā, G, ᾱ) with trivial action ᾱ and an isometric ∗-homomorphism θ : 1(G,A;α) → (G, Ā; ᾱ) = (G) ⊗Ā.