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

Melkiory M.  Aloyce; Santosh  Kumar; Marco  Mpimbo

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