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• W1993706720 abstract "A continuous linear operator T:X→X is hypercyclic if there is an x∈X such that the orbit {Tnx} is dense, and such a vector x is said to be hypercyclic for T. Recent progress show that it is possible to characterize Banach space operators that have a hypercyclic subspace, i.e., an infinite dimensional closed subspace H⊆X of, except for zero, hypercyclic vectors. The following is known to hold: A Banach space operator T has a hypercyclic subspace if there is a sequence (ni) and an infinite dimensional closed subspace E⊆X such that T is hereditarily hypercyclic for (ni) and Tni→0 pointwise on E. In this note we extend this result to the setting of Fréchet spaces that admit a continuous norm, and study some applications for important function spaces. As an application we also prove that any infinite dimensional separable Fréchet space with a continuous norm admits an operator with a hypercyclic subspace." @default.
• W1993706720 created "2016-06-24" @default.
• W1993706720 creator A5067272587 @default.
• W1993706720 date "2006-07-01" @default.
• W1993706720 modified "2023-09-23" @default.
• W1993706720 title "Hypercyclic subspaces for Fréchet space operators" @default.
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• W1993706720 doi "https://doi.org/10.1016/j.jmaa.2005.06.042" @default.
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