Norm Transitive Semigroups on Operator Algebra

Let $\mathcal A $ be a semigroup of bounded linear operators on the Banach algebra $B(X)$ for a separable Banach space $X$ . We show the transitivity of $\mathcal A $ with the operator norm topology, implies hypercyclicity with the strong operator topology (SOT) while the converse may not be true. As a consequence, SOT-transitive semigroup of left multiplication operators on $B(X)$ is characterized.