Dynamics of linear operators on non-Archimedean vector spaces

Farrukh Mukhamedov, Otabek Khakimov

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In the present paper we study dynamics of linear operators defined on topological vector space over non-Archimedean valued fields. We give sufficient and necessary conditions of hypercyclicity (resp. supercyclicity) of linear operators on separable F-spaces. It is proven that a linear operator T on topological vector space X is hypercyclic (supercyclic) if it satisfies Hypercyclicity (resp. Supercyclicity) Criterion. We consider backward shifts on c0(Z) and c0(N), respectively, and characterize hypercyclicity and supercyclicity of such kinds of shifts. Finally, we study hypercyclicity, supercyclicity of operators lI +μB, where I is identity and B is backward shift. We note that there are essential differences between the non-Archimedean and real cases.

Original languageEnglish
Pages (from-to)85-105
Number of pages21
JournalBulletin of the Belgian Mathematical Society - Simon Stevin
Volume25
Issue number1
DOIs
Publication statusPublished - Mar 2018

Keywords

  • Backward shift operator
  • Hypercylic operator
  • Non-Archimedean valuation
  • Supercyclic operator

ASJC Scopus subject areas

  • Mathematics(all)

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