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 H, such that the functional sending an operator T to the complex number <Tx, y> is continuous for any vectors x and y in the Hilbert space.

Equivalently, a net T_i ⊂ B(H) of bounded operators converges to T ∈ B(H) in WOT if for all y* in H* and x in H, the net y*(T_ix) converges to y*(Tx).