On the Structure of Supercyclic Operators on the Operator Algebra

For a separable Banach space X, let L denotes the algebra of bounded operators on X endowed with the strong operator topology. In this note we provide a sufficient condition,in terms of open set in the strong operator topology, for a bounded linear mapping acting on L to be supercyclic with this topology. The main result has some useful consequences and make easy the proof of some related results.