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;