ABSTRACT
Recall that a net {T α } of operators in B(H) converges to T ∈ B(H) in the strong-operator topology if and only if ∥(T α − T)x∥ → 0 for every x in H. If T α → T in the strong-operator topology, it is clear that ∥T α x;∥ → ∥Tx∥ and 〈T α x, y〉 → 〈Tx, y〉 for all x and y in H.
