# On topological transitive maps on operator algebras

Document Type: Research Paper

Author

University of Yasouj

Abstract

We consider the transitive linear maps on the operator algebra $B(X)$
for a separable Banach space $X$. We show if a bounded linear map is norm transitive on $B(X)$,
then it must be hypercyclic with strong operator topology. Also we provide a SOT-transitive
linear map without being hypercyclic in the strong operator topology.

Keywords

### History

• Receive Date: 17 April 2010
• Revise Date: 09 September 2010
• Accept Date: 09 September 2010