Spectral gap characterizations of property (T) for II${}_1$ factors

Abstract

For II${}_1$ factors, we show that property (T) is equivalent to weak spectral gap in any inclusion into a larger tracial von Neumann algebra. We also show that not having non-zero almost central vectors in weakly mixing bimodules characterizes property (T) for II${}_1$ factors, which allows us to obtain a stronger characterization of property (T) where only weak spectral gap in any irreducible inclusion is required.

References in corpus (1)

• Thin II_1 factors with no Cartan subalgebras

Cited by in corpus (1)

• Hypertrace and entropy gap characterizations of property (T) for ${\mathrm{II}}_1$ factors