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Hypercyclic linear fractional composition operators on weighted Dirichlet spacesDαp

Abstract Recently, F. Colonna and R. A. Martinez-Avendano raised the open question that whether or not the weighted Dirichlet spaces D α p can support hypercyclic composition operators when p… Click to show full abstract

Abstract Recently, F. Colonna and R. A. Martinez-Avendano raised the open question that whether or not the weighted Dirichlet spaces D α p can support hypercyclic composition operators when p − 2 α p . In this paper, we investigate the hypercyclicity of composition operators on D α p and partially answer the question. Specifically, under the assumption p − 2 α p , we show that the composition operator induced by a parabolic automorphism or a hyperbolic automorphism of the unit disk is hypercyclic on D α p if p > 3 . Furthermore, the composition operator induced by a hyperbolic non automorphism is hypercyclic on D α p for all p > 1 and p − 1 α p .

Keywords: linear fractional; composition operators; composition; weighted dirichlet; hypercyclic linear

Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2019

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