Dynamical Properties and Some Classes of Non-porous Subsets of Lebesgue Spaces

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Ivković S., Öztop S., Tabatabaie S. M.

Taiwanese Journal of Mathematics, vol.28, no.2, pp.313-328, 2024 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 28 Issue: 2
  • Publication Date: 2024
  • Doi Number: 10.11650/tjm/231204
  • Journal Name: Taiwanese Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.313-328
  • Keywords: hypercyclic vectors, Lebesgue spaces, locally compact groups, locally compact hypergroups, non-σ-porous sets, σ-porous operators
  • Istanbul University Affiliated: Yes

Abstract

In this paper, we introduce several classes of non-σ-porous subsets of a gen-eral Lebesgue space. Also, we study some linear dynamics of operators and show that the set of all non-hypercyclic vectors of a sequences of weighted translation operators on Lp-spaces is not σ-porous.