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 ∈ ℂ ∖{0} of modulus 1 and has similar set of hypercyclic vectors as T. An illustrative example to the main theorem is also provided.