2025/09/23 by Jonathan H. Brown, Brown, Jonathan H., Adam H. Fuller +6
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Rings, Modules, and Algebras #math.OA
paper · pdf · doi:10.48550/arxiv.2509.19148
openalex publication_date 2025/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Let B ⊆ A be a regular inclusion of C*-algebras satisfying the ideal intersection property and with a faithful invariant pseudo-expectation. A complete description of the regular ideals of A is given using the invariant regular ideals of B and the pseudo-expectation. Further, necessary and sufficient conditions are given for a quotient by a regular ideal to preserve the faithful unique pseudo-expectation property. Special attention is given throughout to pseudo-Cartan inclusions, i.e. regular inclusions with the faithful unique pseudo-expectation property, equivalently, having a Cartan envelope. We show that the quotient of a pseudo-Cartan inclusion by a regular ideal is again a pseudo-Cartan inclusion, and we describe the Cartan envelope of the quotient.