hypercyclic operator
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Author(s):  
Quentin Menet

Abstract We show that there exists an invertible frequently hypercyclic operator on $\ell ^1(\mathbb {N})$ whose inverse is not frequently hypercyclic.







2010 ◽  
Vol 7 (1) ◽  
pp. 191-199
Author(s):  
Baghdad Science Journal

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 , .



2007 ◽  
Vol 49 (2) ◽  
pp. 281-290 ◽  
Author(s):  
HÉCTOR N. SALAS

AbstractLet E be a Banach space such that its dual E* is separable. We show that there exists a hypercyclic bounded operator T on E such that its adjoint T* is also hypercyclic on E*. We also exhibit a new kind of dual hypercyclic operator. Thus answers affirmatively two of the questions raised by Henrik Petersson in a recent paper.



2004 ◽  
Vol 41 (4) ◽  
pp. 589-598 ◽  
Author(s):  
Munmun Hazarika ◽  
S.C. Arora






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