On the Structure of Supercyclic Operators on the Operator Algebra

For a separable banach space x, let l denotes the algebraof bounded operators on x endowed with the strong operator topology.in this note we provide a sufficient condition,in terms of open set inthe strong operator topology, for a bounded linear mapping acting onl to be supercyclic with this topology. the main result has some usefulconsequences and make easy the proof of some related results.