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- W2963640441 abstract "We study a hypercyclicity property of linear dynamical systems: a bounded linear operator T acting on a separable infinite-dimensional Banach space X is said to be hypercyclic if there exists a vector x in X such that {T^{n}x : n>0} is dense in X, and frequently hypercyclic if there exists x in X such that for any non empty open subset U of X, the set {n>0 ; T^n x in U} has positive lower density. We prove that if T is a bounded operator on X which has sufficiently many eigenvectors associated to eigenvalues of modulus 1 in the sense that these eigenvectors are perfectly spanning, then T is automatically frequently hypercyclic." @default.
- W2963640441 created "2019-07-30" @default.
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- W2963640441 date "2011-01-01" @default.
- W2963640441 modified "2023-10-16" @default.
- W2963640441 title "A new class of frequently hypercyclic operators" @default.
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- W2963640441 doi "https://doi.org/10.1512/iumj.2011.60.4350" @default.
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