Weak operator topology
Weak topology on function spaces / From Wikipedia, the free encyclopedia
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In functional analysis, the weak operator topology, often abbreviated WOT,[1] is the weakest topology on the set of bounded operators on a Hilbert space , such that the functional sending an operator to the complex number is continuous for any vectors and in the Hilbert space.
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Explicitly, for an operator there is base of neighborhoods of the following type: choose a finite number of vectors , continuous functionals , and positive real constants indexed by the same finite set . An operator lies in the neighborhood if and only if for all .
Equivalently, a net of bounded operators converges to in WOT if for all and , the net converges to .