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On hypercyclicity and supercyclicity criteria. (English) Zbl 1071.47007
In this interesting paper, the authors show that the hypercyclicity criterion coincides with other existing hypercyclicity criteria and prove that a wide class of hypercyclic operators satisfy the criterion. The obtained results extend earlier work of several authors. They also unify the different versions of the supercyclicity criterion and show that operators with dense generalised kernel and dense range are supercyclic.

MSC:
47A16 Cyclic vectors, hypercyclic and chaotic operators
47A11 Local spectral properties of linear operators
46A04 Locally convex Fréchet spaces and (DF)-spaces
46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
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