Strong-star operator topology
= Strong-star operator topology
{title2=$T_i\xi\to T\xi,\quad T_i^*\xi\to T^*\xi\quad(\xi\in H)$}
= Strong-star topology
{synonym}
This topology on <bounded operators> is generated by the seminorms $(\|T\xi\|^2+\|T^*\xi\|^2)^{1/2}$. A net converges exactly when both it and its adjoint net converge in the <strong operator topology>. It is the topology used in the full-unit-ball version of the <Kaplansky density theorem>.