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Hypercyclictty and Countable Hypercyclicity for Adjoint of Operators | ||
| Baghdad Science Journal | ||
| Article 1, Volume 7, Issue 0, 2010, Pages 191-199 | ||
| Authors | ||
| Hiba F. Al-Janaby; Buthainah A. Ahmed | ||
| Abstract | ||
| 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 , . | ||
| Keywords | ||
| operator; hypercyclic; countably hypercyclic; single valued extension property; Bishop; decomposition property | ||
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