Unique conditional expectations for abelian C^*-inclusions

2016/03/26 by Zarikian, Vrej
#46L05 #46L07 #54C10 #60B05 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1603.08110

Abstract

Let D ⊆ A be an inclusion of unital abelian C^*-algebras. In this note we characterize (in topological terms) when there is a unique conditional expectation E:A → D, at least when A is separable. As an application, we provide the first example of an inclusion with a unique conditional expectation, but multiple pseudo-expectations (in the sense of Pitts).

Related

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• A Generalization of Whyburn's Theorem, and Aperiodicity for Abelian\n C*-Inclusions