Hypercyclicity of Shifts on Weighted ${\mathbf{L}}^p$ Spaces of Directed Trees

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 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.

References in corpus (3)

• Multiplication operators on the weighted Lipschitz space of a tree
• Multiplication operators on the iterated logarithmic Lipschitz spaces of a tree
• Multiplication operators between Lipschitz-type spaces on a tree

Cited by in corpus (8)

• Hypercyclicity of composition operators on discrete weighted Banach spaces
• On several dynamical properties of shifts acting on directed trees
• Reduced commutativity of moduli of operators
• A Shimorin-type analytic model on an annulus for left-invertible operators and applications
• Generalized multipliers for left-invertible operators and applications
• Disjoint hypercyclic weighted pseudo-shift operators generated by different shifts
• Frequently hypercyclic composition operators on the little Lipschitz space of a rooted tree
• The forward and backward shift on the Lipschitz space of a tree