Notes about the hypercyclicity criterion
ISSN: 0139-9918
Datum der Publikation: 2003
Ausgabe: 53
Nummer: 3
Seiten: 313-319
Art: Artikel
Andere Publikationen in: Mathematica Slovaca
Zusammenfassung
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.