Strong operator topology on a $C^*$-algebra?

Question

As far as I know, the Strong Operator Topology (SOT) is defined for the space of operators $B(H)$ for any Hilbert space H. The paper I am reading implicitly make references to the 'fact' that we can endow any $C^*$-algebra $A$ with the strong operator topology. How do we do that? The most natural way that I can think of is the topology induced by the Gelfand-Naimark-Segal theorem. Suppose that $\pi: A\to B(H)$ is the representation that realizes $A$ as an operator algebra (by GNS), do we define the strong operator open sets in $A$ via inverse images $\pi^{-1}(V)$ where $V\subseteq B(H)$ is strong operator open in $B(H)$?

Answer 1

No, because there is no "the" representation that makes $A$ an operator algebra. As mentioned by @JustDroppedIn, there are usually different representations.