Hypercyclictty and Countable Hypercyclicity for Adjoint of Operators

• Main Author: Baghdad Science Journal
• Format: Article
• Language: Arabic
• Published: College of Science for Women, University of Baghdad 2010-03-01
• Series: Baghdad Science Journal
• Subjects: " operator, hypercyclic, countably hypercyclic, single valued extension property (SVEP), Bishop's property , decomposition property ."
• Online Access: http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/2887

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 , .