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<p>We extend the concept of average expansivity for operators on Banach spaces to operators on arbitrary locally convex spaces. We obtain complete characterizations of the average expansive weighted shifts on Fréchet sequence spaces. Moreover, we give a partial answer to a problem proposed by Bernardes et al. (J Funct Anal 288(2):51, Paper No. 110696, 2025), by obtaining complete characterizations of the uniformly expansive weighted shifts on Köthe sequence spaces. Some general properties of the various concepts of expansivity in linear dynamics and several concrete examples are also presented.</p>

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On notions of expansivity for operators on locally convex spaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月5日

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  • Nilson C. Bernardes Jr.,
  • Félix Martínez-Giménez,
  • Francisco Rodenas

摘要

We extend the concept of average expansivity for operators on Banach spaces to operators on arbitrary locally convex spaces. We obtain complete characterizations of the average expansive weighted shifts on Fréchet sequence spaces. Moreover, we give a partial answer to a problem proposed by Bernardes et al. (J Funct Anal 288(2):51, Paper No. 110696, 2025), by obtaining complete characterizations of the uniformly expansive weighted shifts on Köthe sequence spaces. Some general properties of the various concepts of expansivity in linear dynamics and several concrete examples are also presented.