On the spectrum of frequently hypercyclic operators
Data(s) |
01/01/2009
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Resumo |
A bounded linear operator $T$ on a Banach space $X$ is called frequently hypercyclic if there exists $x\in X$ such that the lower density of the set $\{n\in\N:T^nx\in U\}$ is positive for any non-empty open subset $U$ of $X$. Bayart and Grivaux have raised a question whether there is a frequently hypercyclic operator on any separable infinite dimensional Banach space. We prove that the spectrum of a frequently hypercyclic operator has no isolated points. It follows that there are no frequently hypercyclic operators on all complex and on some real hereditarily indecomposable Banach spaces, which provides a negative answer to the above question. |
Formato |
application/pdf |
Identificador | |
Idioma(s) |
eng |
Direitos |
info:eu-repo/semantics/restrictedAccess |
Fonte |
Shkarin , S 2009 , ' On the spectrum of frequently hypercyclic operators ' Proceedings of the American Mathematical Society , vol 137 , no. 1 , pp. 123-134 . |
Palavras-Chave | #/dk/atira/pure/subjectarea/asjc/2600 #Mathematics(all) #/dk/atira/pure/subjectarea/asjc/2600/2604 #Applied Mathematics |
Tipo |
article |