Strong operator topology

Summary

The strong operator topology is the topology of pointwise convergence on the bounded operators on a Hilbert space. A net $T_i$ converges to $T$ when $T_i x \to T x$ in norm for every vector $x$. It lies between the weak operator topology and the norm topology. It is the natural topology for limits such as partial sums of orthogonal projections and for one-parameter unitary groups.