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<p>We study hypercyclic or mixing weighted backward shift operators on the little Hardy spaces and the little Lipschitz spaces over rooted locally finite directed trees in the sense of Muthukumar–Ponnusamy and Colonna–Easley. Our results generalize some theorems due to Ángeles-Romero, Martínez-Avendaño and Rivera-Guasco concerning weight-one backward shift operators on these spaces and allow us to discuss the hypercyclicity of these operators in a unified framework.</p>

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Hypercyclicity of Weighted Backward Shifts on the Little Hardy and the Little Lipschitz Spaces Over Directed Trees

  • 期刊论文

  • 发表日期：

    2025年11月16日

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  • Kazuhiro Kawamura

摘要

We study hypercyclic or mixing weighted backward shift operators on the little Hardy spaces and the little Lipschitz spaces over rooted locally finite directed trees in the sense of Muthukumar–Ponnusamy and Colonna–Easley. Our results generalize some theorems due to Ángeles-Romero, Martínez-Avendaño and Rivera-Guasco concerning weight-one backward shift operators on these spaces and allow us to discuss the hypercyclicity of these operators in a unified framework.