Strict comparison and Z-absorption of nuclear C*-algebras

Abstract

For any unital separable simple infinite-dimensional nuclear C*-algebra with finitely many extremal traces, we prove that Z-absorption, strict comparison, and property (SI) are equivalent. We also show that any unital separable simple nuclear C*-algebra with tracial rank zero is approximately divisible, and hence is Z-absorbing.

14 pages

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Cited by in corpus (11)

• Nuclear dimension and Z-stability
• Nuclear dimension, Z-stability, and algebraic simplicity for stably projectionless C*-algebras
• Tensor products and regularity properties of Cuntz semigroups
• Picard groups of certain stably projectionless C*-algebras
• Trace scaling automorphisms of the stabilized Razak-Jacelon algebra
• Central sequence C*-algebras and tensorial absorption of the Jiang-Su algebra
• Smooth lattice orbits of nilpotent groups and strict comparison of projections
• The Cuntz-Toeplitz algebras have nuclear dimension one
• Rokhlin dimension: absorption of model actions
• On the bundle of KMS state spaces for flows on a Z-absorbing C*-algebra
• Decomposable approximations and approximately finite dimensional C*-algebras