On topological transitive maps on operator algebras

Document Type : Research Paper


University of Yasouj


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.