Unique conditional expectations for abelian $C^*$-inclusions

Vrej Zarikian

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arXiv · 1603.08110

Unique conditional expectations for abelian $C^*$-inclusions

Vrej Zarikian

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Abstract

Let $D \subseteq A$ be an inclusion of unital abelian $C^*$-algebras. In this note we characterize (in topological terms) when there is a unique conditional expectation $E:A \to D$, 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).

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Vrej Zarikian. 2016-03-26. Unique conditional expectations for abelian $C^*$-inclusions. https://arxiv.org/abs/1603.08110

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