Unique conditional expectations for abelian \(C^\)-inclusions

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...

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Bibliographic Details
Published in:arXiv.org 2016-09
Main Author: Zarikian, Vrej
Format: Article
Language:English
Subjects:
Economic models
Inclusions
Online Access:Get full text
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Summary: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).
ISSN:2331-8422