Ueber unstetige Lösungen in der Variationsrechnung.
Hypercyclic and chaotic weighted shifts
Extending previous results of H. Salas we obtain a characterisation of hypercyclic weighted shifts on an arbitrary F-sequence space in which the canonical unit vectors form a Schauder basis. If the basis is unconditional we give a characterisation of those hypercyclic weighted shifts that are even chaotic.
The Hypercyclicity Criterion for sequences of operators
We show that under no hypotheses on the density of the ranges of the mappings involved, an almost-commuting sequence (Tₙ) of operators on an F-space X satisfies the Hypercyclicity Criterion if and only if it has a hereditarily hypercyclic subsequence , and if and only if the sequence (Tₙ ⊕ Tₙ) is hypercyclic on X × X. This strengthens and extends a recent result due to Bès and Peris. We also find a new characterization of the Hypercyclicity Criterion in terms of a condition introduced by Godefroy...
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