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

2021-03-08

Issue

Vol. 45 No. 3 (2019)

Section

Articles