Unique Pseudo-Expectations for Dynamical C^*-Inclusions

2026/08/01 by Vrej Zarikian
Mathematics · #math.OA #msc:46L07 #msc:46L55

paper · pdf

31 pages, comments welcome

arxiv created 2026/08/01 · arxiv updated 2026/08/04

Abstract

Let (A,G,α) be a C^*-dynamical system. Unique extension properties for the C^*-inclusion A ⊆ A \rtimes_α,r G have been studied extensively. In this paper, we investigate unique extension properties for some other natural ``dynamical'' C^*-inclusions, namely: \bullet C_r^*(G) ⊆ A \rtimes_α,r G; \bullet A^G ⊆ A, where A^G is the fixed-point subalgebra; \bullet Z(A)^c ⊆ A \rtimes_α,r G, where Z(A)^c = Z(A)' ∩ (A \rtimes_α,r G) is the relative commutant of the center. Our hope is that a larger selection of examples will enable progress on some lingering open problems, in particular (1) the relationship between aperiodicity and the unique pseudo-expectation property and (2) the relationship between the faithful unique pseudo-expectation property and norming.

Citations

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