On Local Finite Dimensional Approximation of C∗-algebras

  title={On Local Finite Dimensional Approximation of C∗-algebras},
  author={Sorin Popa and To Ed Effros},
Recall that a C∗-algebra A is called quasidiagonal if it can be represented faithfully on a Hilbert space H such that there exist finite dimensional vector subspaces Hi ⊂ H, with Hi ↗ H and lim i ‖[projHi , x]‖ = 0, ∀ x ∈ A (see e.g., [V2]). By Voiculescu’s theorem ([V1]), if A is simple then this property doesn’t in fact depend on the Hilbert space on which A is represented, so that it can be reformulated in terms of the following local finite dimensional approximation property: A simple C… CONTINUE READING