Abstract
Let Hbe an infinite dimensional separable complex Hilbert space and let Tє B(H), where B(H) is the Banach algebra of all bounded linear operators on H. In this paper we prove the following results. If T є B(H) is a θ- operator, then 1. T * is a hypercyclic operator if and only if σ(Τ|_M) ∩D ≠ ф and σ(Τ|_M) ∩(C\D) ≠ ф for every hyperinvariant subspace M of T. 2. If T is a pure, then T* is a countably hypercyclic operator if and only if σ(Τ|_M) ∩(C\D) ≠ ф and σ(Τ) ∩D ≠ ф for every hyperinvariant subspace M of T. 3. T* has a bounded set with dense orbit if and only if for every hyperinvariant subspace M of Τ, σ(Τ_M)∩(C\D)≠ф.
Article Type
Article
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
How to Cite this Article
Ahmed, Buthainah A. and Al-Janaby, Hiba F.
(2010)
"Hypercyclictty and Countable Hypercyclicity for Adjoint of θ -Operators,"
Baghdad Science Journal: Vol. 7:
Iss.
1, Article 39.
DOI: https://doi.org/10.21123/bsj.2010.7.1.191-199
