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Limits of hypercyclic and supercyclic operators. (English) Zbl 0758.47016
Let $$T$$ be a bounded linear operator on a complex, separable infinite dimensional Hilbert space $$H$$, and let $$y\in H$$. The orbit of $$y$$ under $$T$$ is the set $$\text{Orb}(T,y):=\{y,Ty,T^ 2y,\dots\}$$. A vector $$y\in H$$ is called hypercyclic (resp., supercyclic) for $$T$$, if $$\text{Orb}(T,y)$$ is dense in $$H$$ (resp., if the set of scalar multiples of $$\text{Orb}(T,y)$$ is dense in $$H$$). The author obtains a spectral characterization of the norm closure of the class of all hypercyclic operators on $$H$$, and describes the structure of the set of all hypercyclic vectors of a given hypercyclic operator. Analogous results are obtained for supercyclic operators and vectors.

MSC:
 47A65 Structure theory of linear operators
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References:
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