Weak operator topology

In functional analysis, the weak operator topology, often abbreviated WOT, is the weakest topology on the set of bounded operators on a Hilbert space such that the functional sending an operator T to the complex number <math>\langle Tx,y\rangle<math> is continuous for any vectors x and y in the Hilbert space.

The WOT is weaker than the strong operator topology and weaker than the norm topology. The weak-star topology is stronger than the WOT.

The linear functionals on the set of bounded operators on a Hilbert space which are continuous in the strong operator topology are precisely those which are continuous in the WOT. Because of this fact, the closure of a convex set of operators in the WOT is the same as the closure of that set in the SOT.

The WOT and the weak-star topology agree on bounded sets.