Stability under small tracial perturbations for C*-algebras

Tatiana Shulman (Instytut Matematyczny Polskiej Akademii Nauk)

Tuesday 28th February, 2017 16:00-17:00 Maths 203


We consider tracial stability, which requires that tuples of elements of a C*-algebra with a trace that nearly satisfy the relation are close to tuples that actually satisfy the relation. Here both "near" and "close" are in terms of the associated 2-norm from the trace, e.g., the Hilbert-Schmidt norm for matrices. Precise definitions are stated in terms of liftings from tracial ultraproducts of C*-algebras. We will discuss matricial tracial stability and stability with respect to tracial norms on real rank zero C*-algebras. In particular we will completely characterize matricial tracial stability for nuclear C*-algebras in terms of certain approximation properties for traces. We will discuss obstructions for tracial stability of  non-nuclear C*-algebras. We will also discuss tracial stability for groups. This is a joint work with Don Hadwin.

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