• Corpus ID: 221703061

Diffuse traces and Haar unitaries

  title={Diffuse traces and Haar unitaries},
  author={Hannes Thiel},
  journal={arXiv: Operator Algebras},
  • Hannes Thiel
  • Published 15 September 2020
  • Mathematics
  • arXiv: Operator Algebras
We show that a tracial state on a unital C*-algebra admits a Haar unitary if and only if it is diffuse, if and only if it does not dominate a tracial functional that factors through a finite-dimensional quotient. It follows that a unital C*-algebra has no finite-dimensional representations if and only if each of its tracial states admits a Haar unitary. More generally we study the situation for nontracial states. In particular, we show that every state on a unital, simple, infinite-dimensional… 
1 Citations
Nowhere scattered C*-algebras
We say that a C∗-algebra is nowhere scattered if none of its quotients contains a minimal projection. We characterize this property in various ways, by topological properties of the spectrum, by


The stable rank of some free product C*-algebras
It is proved that the reduced group C*-algebra C*_{red}(G) has stable rank one (i.e. its group of invertible elements is a dense subset) if G is a discrete group arising as a free product G_1*G_2
Perturbation of Hausdorff Moment Sequences, and an Application to the Theory of C*-Algebras of Real Rank Zero
We investigate the class of unital C*-algebras that admit a unital embedding into every unital C*-algebra of real rank zero, that has no finite-dimensional quotients. We refer to a C*-algebra in this
Cuntz semigroups of ultraproduct C∗ ‐algebras
We prove that the category of abstract Cuntz semigroups is bicomplete. As a consequence, the category admits products and ultraproducts. We further show that the scaled Cuntz semigroup of the
Free Products of C ∗ -Algebras
Small ("spatial") free products of C*-algebras are constructed. Under certain conditions they have properties similar to those proved by Paschke and Salinas for the algebras C,*(GI * G2) where G1, G2
States and automorphism groups of operator algebras
Suppose that a group of automorphisms of a von Neumann algebraM, fixes the center elementwise. We show that if this group commutes with the modular (KMS) automorphism group associated with a normal
The selfadjoint operators of a von Neumann algebra form a conditionally complete lattice
The bounded resolutions of the identity in a von Neumann algebra can be ordered by I Es(u) } - ET(U), uER. The selfadjoint operators in the algebra are partially ordered by this relation and are
Free products of hyperfinite von Neumann algebras and free dimension
The free product of an arbitrary pair of finite hyperfinite von Neumann algebras is examined, and the result is determined to be the direct sum of a finite dimensional algebra and an interpolated