Strong Operator Topology
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In functional analysis, a branch of mathematics, the strong operator topology, often abbreviated SOT, is the weakest locally convex topology on the set of bounded operators on a Hilbert space (or, more generally, on a Banach space) such that the evaluation map sending an operator T to the real number Tx is continuous for each vector x in the Hilbert space. The SOT is stronger than the weak operator topology and weaker than the norm topology. The SOT lacks some of the ...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In functional analysis, a branch of mathematics, the strong operator topology, often abbreviated SOT, is the weakest locally convex topology on the set of bounded operators on a Hilbert space (or, more generally, on a Banach space) such that the evaluation map sending an operator T to the real number Tx is continuous for each vector x in the Hilbert space. The SOT is stronger than the weak operator topology and weaker than the norm topology. The SOT lacks some of the nicer properties that the weak operator topology has, but being stronger, things are sometimes easier to prove in this topology. It is more natural too, since it is simply the topology of pointwise convergence for an operator.
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