Geodesic
On the norm-closure of the class of hypercyclic operators
Annales Polonici Mathematici, Tome 65 (1996) no. 2, pp. 157-161

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Let T be a bounded linear operator acting on a complex, separable, infinite-dimensional Hilbert space and let f: D → ℂ be an analytic function defined on an open set D ⊆ ℂ which contains the spectrum of T. If T is the limit of hypercyclic operators and if f is nonconstant on every connected component of D, then f(T) is the limit of hypercyclic operators if and only if $f(σ_{W}(T)) ∪ {z ∈ ℂ: |z| = 1}$ is connected, where $σ_{W}(T)$ denotes the Weyl spectrum of T.
DOI : 10.4064/ap-65-2-157-161
Keywords: hypercyclic operators

Christoph Schmoeger 1

1 
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Christoph Schmoeger. On the norm-closure of the class of hypercyclic operators. Annales Polonici Mathematici, Tome 65 (1996) no. 2, pp. 157-161. doi: 10.4064/ap-65-2-157-161

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