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

  • Melkiory Aloyce Department of Economics and Statistics, Moshi Co-operative University
  • Santosh Kumar Department of Mathematics, University of Dar es Salaam
  • Marco Mpimbo Department of Mathematics, University of Dar es Salaam
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.

Keywords: Non-normable  Fréchet space; Hypercyclic operator; Supercyclic operator;

Published
2019-12-22
Section
Articles

Journal Identifiers


eISSN: 2507-7961
print ISSN: 0856-1761