Herrero's Approximation Problem for Quasidiagonal Operators

Nathanial P. Brown

Let $T$ be a quasidiagonal operator on a separable Hilbert space. It is shown that there exists a sequence of operators $\{ T_n \}$ such that $\dim C^*(T_n) < \infty$ and $\|T -T_n\|\to 0$ if and only if $C^*(T)$ is exact.