Science Fair Project Encyclopedia
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
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details