Norming in discrete crossed products

Let G↷A be an action of a discrete group on a unital C∗-algebra by ∗-automorphisms. In this note, we give two sufficient dynamical conditions for the C∗-inclusion A⊆A⋊rG to be norming in the sense of Pop, Sinclair, and Smith. As a consequence of our results, when A is separable or simple, the inclusion A⊆A⋊rG is norming, provided it has a unique pseudo-expectation in the sense of Pitts.

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Publication Details

Journal
Illinois Journal of Mathematics
Published
2024-12-01
DOI
https://doi.org/10.1215/00192082-11621162
Primary Topic
Advanced Operator Algebra Research
Type
article
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article

Norming in discrete crossed products

Vrej Zarikian, David R. Pitts, Roger R. Smith
Illinois Journal of Mathematics
Advanced Operator Algebra Research
article

Norming in discrete crossed products

Vrej Zarikian, David R. Pitts, Roger R. Smith
article en

Abstract

Let G↷A be an action of a discrete group on a unital C∗-algebra by ∗-automorphisms. In this note, we give two sufficient dynamical conditions for the C∗-inclusion A⊆A⋊rG to be norming in the sense of Pop, Sinclair, and Smith. As a consequence of our results, when A is separable or simple, the inclusion A⊆A⋊rG is norming, provided it has a unique pseudo-expectation in the sense of Pitts.

Illinois Journal of MathematicsVol. 68(4)
University of Nebraska–Lincoln (US), United States Naval Academy (US), Texas A&M University (US)
Openalex Percentile: Top 58%
Advanced Operator Algebra Research
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