Notes about the hypercyclicity criterion
ISSN: 0139-9918
Année de publication: 2003
Volumen: 53
Número: 3
Pages: 313-319
Type: Article
D'autres publications dans: Mathematica Slovaca
Résumé
A Banach space operator T is said to be hypercyclic if there exists a vector x such that the orbit {Tn x} is dense in the space. The most used tool to discover hypercyclic operators is known as the Hypercyclicity Criterion. Given an operator T satisfying the Hypercyclicity Criterion, we characterize the subsequences of natural numbers {nk} for which we can assert that the sequence of powers {Tnfc} also satisfies it. In order to show that, some equivalent conditions of the Hypercyclicity Criterion are studied. Finally as a consequence of this analysis we show that hypercyclic operators with a dense subset of almost periodic vectors satisfy the Hypercyclicity Criterion.