Hypercyclictty and Countable Hypercyclicity for Adjoint of Operators (Baghdad Science Journal, 2025)
Let be an infinite dimensional separable complex Hilbert space and let , where is the Banach algebra of all bounded linear operators on . In this paper we prove the following results.If is a operator, then 1. is a hypercyclic operator if and only if D and for every hyperinvariant subspace of .2. If is a pure, then is a countably hypercyclic operator if and only if and for every hyperinvariant subspace of .3. has a bounded set with dense orbit if and only if for every hyperinvariant subspace of , .