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Tanzania Journal of Science

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

Melkiory Aloyce, Santosh Kumar, Marco Mpimbo

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;




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