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 ${\displaystyle H}$, such that the functional sending an operator ${\displaystyle T}$ to the complex number ${\displaystyle \langle Tx,y\rangle }$ is continuous for any vectors ${\displaystyle x}$ and ${\displaystyle y}$ in the Hilbert space.

...
Wikipedia