Strong operator topology

In functional analysis, a branch of mathematics, the strong operator topology, often abbreviated SOT, is the locally convex topology on the set of bounded operators on a Hilbert space H induced by the seminorms of the form , as x varies in H.

Equivalently, it is the coarsest topology such that the evaluation maps (taking values in H) are continuous for each fixed x in H. The equivalence of these two definitions can be seen by observing that a subbase for both topologies is given by the sets (where T₀ is any bounded operator on H, x is any vector and ε is any positive real number).