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 Ti ⊂ 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*(Tix) converges to y*(Tx).
Read more about Weak Operator Topology: Relationship With Other Topologies On B(H), Other Properties
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—Lao-Tzu (6th century B.C.)