Ultraweak topology

Summary

The ultraweak topology, also called the $\sigma$-weak topology, is a topology on the bounded operators $B(H)$ on a Hilbert space $H$. It is the weak-$*$ topology that comes from viewing $B(H)$ as the dual of the space of trace class operators. It is finer than the weak operator topology but agrees with it on bounded sets. The linear functionals that are continuous for it are exactly the normal functionals, which makes it the intrinsic topology of a von Neumann algebra.