Regular ideals under the ideal intersection property

Ruy Exel

Regular ideals under the ideal intersection property

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arxiv 2301.10073 v1 pith:7QIFIYCZ submitted 2023-01-24 math.OA

Ruy Exel This is my paper · ORCID

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keywords algebraidealsregularbooleanidealintersectionpropertyaxiom

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abstract

The goal of this short note is to prove that when $A$ is a closed *-subalgebra of a C*-algebra $B$ satisfying the ideal intersection property plus a mild axiom (INV), then the map $J\mapsto J\cap A$ establishes an isomorphism from the boolean algebra of all regular ideals of $B$ to the boolean algebra of all regular, invariant ideals of $A$.

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Regular ideals, Ideal Intersections and Quotients II
math.OA 2025-09 accept novelty 6.0 of 10

Regular inclusions with a faithful invariant pseudo-expectation have their regular ideals determined by invariant regular ideals of the subalgebra, and quotients by regular ideals preserve the pseudo-Cartan property a...

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