For weighted backward shifts on rooted directed trees, the paper proves that a hypercyclic algebra exists exactly when a stronger supremum growth condition holds on ell-p spaces, and it shows hypercyclicity does not imply algebrability on tree ell-p spaces.
Hypercyclic shifts on lattice graphs
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abstract
Recently K.-G. Grosse-Erdmann and D. Papathanasiou described hypercyclic shifts in weighted spaces on directed trees. In this note we discuss several simple examples of graphs which are not trees, e.g., the lattice graphs, and study hypercyclicity of the corresponding backward shifts.
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Hypercyclic algebras for weighted shifts on trees
For weighted backward shifts on rooted directed trees, the paper proves that a hypercyclic algebra exists exactly when a stronger supremum growth condition holds on ell-p spaces, and it shows hypercyclicity does not imply algebrability on tree ell-p spaces.