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The tracial Rokhlin property for an inclusion of unital Cβˆ—C^*-algebras

Abstract

We introduce and study a notion of Rokhlin property for an inclusion of unital Cβˆ—C^*-algebras which could have no projections like the Jiang-Su algebra. We also introduce a notion of approximate representability and show a duality between them. We demonstrate the importance of these notions by showing the permanence of the tracial Z\mathcal{Z}-absorbingness and the strict comparison property.Comment: This is our third joint paper. 25 page

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