Regular ideals under the ideal intersection property

Ruy Exel

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arXiv · 2301.10073

Regular ideals under the ideal intersection property

Ruy Exel

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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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Ruy Exel. 2023-01-24. Regular ideals under the ideal intersection property. https://arxiv.org/abs/2301.10073

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