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

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;

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;