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Hypertrace and entropy gap characterizations of property (T) for II 1 factors

Journal of Functional Analysis, ISSN: 0022-1236, Vol: 287, Issue: 6, Page: 110530
2024
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Article Description

We establish a hypertrace characterization of property (T) for II1 factors: Given a II1 factors M, M does not have property (T) if and only if there exists a von Neumann algebra A with M⊂A such that A admits a M -hypertrace but no normal hypertrace. For M without property (T), such an inclusion M⊂A also admits almost vanishing Furstenberg entropy. With the same construction of M⊂A, we also establish similar characterizations of Haagerup property for II1 factors.

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