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Supercyclic and Hypercyclic Generalized Weighted Backward Shifts over a Non-Archimedean c 0 ( N ) Space

Author

Listed:
  • Farrukh Mukhamedov

    (Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al Ain P.O. Box 15551, United Arab Emirates
    Department of Algebra and Analysis, Institute of Mathematics Named after V.I.Romanovski, 4, University Str., Tashkent 100125, Uzbekistan)

  • Otabek Khakimov

    (Department of Algebra and Analysis, Institute of Mathematics Named after V.I.Romanovski, 4, University Str., Tashkent 100125, Uzbekistan
    AKFA University, 1st Deadlock 10, Kukcha Darvoza, Tashkent 100095, Uzbekistan)

  • Abdessatar Souissi

    (Department of Accounting, College of Business Management, Qassim University, Buraydah 52571, Saudi Arabia)

Abstract

In the present paper, we propose to study generalized weighted backward shifts B B over non-Archimedean c 0 ( N ) spaces; here, B = ( b i j ) is an upper triangular matrix with sup i , j | b i j | < ∞ . We investigate the sypercyclic and hypercyclic properties of B B . Furthermore, certain properties of the operator I + B B are studied as well. To establish the hypercyclic property of I + B B we have essentially used the non-Archimedeanity of the norm which leads to the difference between the real case.

Suggested Citation

  • Farrukh Mukhamedov & Otabek Khakimov & Abdessatar Souissi, 2021. "Supercyclic and Hypercyclic Generalized Weighted Backward Shifts over a Non-Archimedean c 0 ( N ) Space," Mathematics, MDPI, vol. 9(22), pages 1-14, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:22:p:2986-:d:685370
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