Erratum to "Full and reduced C*-coactions". Math. Proc. Camb. Phil. Soc. 116 (1994), 435--450

TL;DR

This paper corrects a previous proposition regarding the nondegeneracy of full coactions on C*-algebras and discusses the current understanding of their relationships.

Contribution

It amends an earlier statement about coaction nondegeneracy and clarifies the current knowledge gaps in the theory of C*-coactions.

Findings

The original proof of the reverse implication was incorrect.

The authors summarize the current state of knowledge.

Open questions remain about the relationships between different types of coactions.

Abstract

This short note amends Proposition 2.5 of the named article, which states that a full coaction of a locally compact group on a C*-algebra is nondegenerate if and only if its normalization is. The proof given there of the reverse implication is incorrect and, unfortunately, we have been unable to find a correct proof. Instead, we summarize the current state of our knowledge of the relationships between nondegeneracy of normal, reduced, and generic C*-coactions.