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 UniversityFollow
Santosh Kumar, Department of Mathematics, University of Dar es Salaam, P. O. Box 35062, Dar es Salaam, Tanzania.Follow
Marco Mpimbo, Department of Mathematics, University of Dar es Salaam, P. O. Box 35062, Dar es Salaam, Tanzania.Follow

Section

Physical Sciences

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.

Recommended Citation

Aloyce, Melkiory M.; Kumar, Santosh; and Mpimbo, Marco (2019) "On Scalar Multiples of Hypercyclic Operators on Non-normable and Separable Fréchet Spaces," Tanzania Journal of Science: Vol. 45: Iss. 3, Article 12.
Available at:https://doi.org/10.65085/2507-7961.1696