Weak operator topology

Summary

The weak operator topology is a topology on the bounded operators on a Hilbert space. In it, a net of operators converges when all its matrix coefficients $\langle T x, y \rangle$ converge. It is much coarser than the norm topology, so more sets are compact and more nets converge. It is the topology used to define von Neumann algebras, and its closed unit ball is compact.