On Scalar Multiples of Hypercyclic Operators on Non-normable and Separable Fréchet Spaces

Authors

  • Melkiory M. Aloyce Department of Economics and Statistics, Moshi Co-operative University
  • Santosh Kumar Department of Mathematics, University of Dar es Salaam, P. O. Box 35062, Dar es Salaam, Tanzania.
  • Marco Mpimbo Department of Mathematics, University of Dar es Salaam, P. O. Box 35062, Dar es Salaam, Tanzania.

Keywords:

Non-normable Fréchet space, Hypercyclic operator, Supercyclic operator

Abstract

In this paper, we proved that if F is a non-normable and separable Fréchet space without a continuous norm, then there exists an operator T L (F) such that λ T is hypercyclic for any λ   {0} of modulus 1 and has similar set of hypercyclic vectors as T. An illustrative example to the main theorem is also provided.

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Published

08-03-2021

How to Cite

Aloyce, M. M. ., Kumar, S. ., & Mpimbo, M. . (2021). On Scalar Multiples of Hypercyclic Operators on Non-normable and Separable Fréchet Spaces. Tanzania Journal of Science, 45(3), 431–438. Retrieved from https://tjs.udsm.ac.tz/index.php/tjs/article/view/211

Issue

Vol. 45 No. 3 (2019)

Section

Articles