Dixmier approximation and symmetric amenability for C*-algebras

By Nathanial P. Brown Narutaka Ozawa. 2013

58 citations recorded by the source corpus.

We study some general properties of tracial C*-algebras. In the first part, we consider Dixmier type approximation theorem and characterize symmetric amenability for C*-algebras. In the second part, we consider continuous bundles of tracial von Neumann algebras and classify some of them.

Subfields: Algebra and Number Theory, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/093210794a025973127f567eb2db2d2200942cdd

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In Algebra and Number Theory

1. Samuel Evington
2. Jorge Castillejos
3. Stuart White
4. Aaron Tikuisis
5. Yasuhiko Sato
6. W. Winter
7. N. Brown
8. J. Bosa

In Mathematical Physics

1. Samuel Evington
2. Jorge Castillejos
3. Stuart White
4. Aaron Tikuisis
5. W. Winter
6. Yasuhiko Sato
7. G'abor Szab'o
8. N. Brown

In Statistical and Nonlinear Physics

1. Samuel Evington
2. Jorge Castillejos
3. Stuart White
4. Yasuhiko Sato
5. Aaron Tikuisis
6. N. Brown
7. J. Bosa
8. W. Winter

Citations in the corpus

• STRUCTURE OF NUCLEAR C*-ALGEBRAS: FROM QUASIDIAGONALITY TO CLASSIFICATION AND BACK AGAIN (2017, methodology): “ in addition that every trace is quasidiagonal (by Theorem 3.7 this is automatic when Asatisfies the UCT). For these last results, the ground was prepared by Ozawa’s theory of von Neumann bundles from [39]. In upcoming work, Jorge Castillejos, Sam Evington, Aaron Tikuisis, Stuart White and I will sho”
• Covering Dimension of C*-Algebras and 2-Coloured Classification (2015, background): “15Formally, as in [65], one considers the quotient C-algebra of the norm bounded ‖ · ‖2,u-Cauchy sequences, modulo the ideal of ‖ · ‖2,u-null sequences.”
• Subalgebras of simple AF-algebras (2018, unknown): “By Theorem 8 in [61], the unique trace on Bω is the trace τBω induced by τB.”
• Nuclear dimension of simple $$\mathrm {C}^*$$-algebras (2019, methodology): “he continuous functions on the extreme boundary, and we only need to use extremal traces in the compactness argument to obtain the Ui’s. The required (ei)k i=1 arise via Ozawa’s theory ofW ∗-bundles ([47]): one takes a partition of unity (fi)k i=1 in C(∂eT(A)) subordinate to the cover (Ui)ki=1 and t”