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Abstract In this paper, we study the hypercyclicity of forward and backward shifts on weighted L p spaces of a directed tree. In the forward case, only the trivial trees… Click to show full abstract
Abstract In this paper, we study the hypercyclicity of forward and backward shifts on weighted L p spaces of a directed tree. In the forward case, only the trivial trees may support hypercyclic shifts, in which case the classical results of Salas [21] apply. For the backward case, nontrivial trees may support hypercyclic shifts. We obtain necessary conditions and sufficient conditions for hypercyclicity of the backward shift and, in the case of a rooted tree on an unweighted space, we show that these conditions coincide.
Keywords:
spaces directed;
hypercyclicity;
case;
shifts weighted;
hypercyclicity shifts;
weighted spaces
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2017
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Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!