On the norm-closure of the class of hypercyclic operators

Volume 65 / 1997

Christoph Schmoeger Annales Polonici Mathematici 65 (1997), 157-161 DOI: 10.4064/ap-65-2-157-161


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.


  • Christoph Schmoeger

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