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 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. See also weak topologyweak-star topologyTopologies on the set of operators on a Hilbert space
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