An infinite-dimensional subspace of a non-normable and separable frechet space

Abstract

In this paper, we proved that if F is a non-normable and separable Fr´echet space, then there exists an infinite-dimensional subspace A ⊂ L(F) such that any non-zero operator T ∈ A is hypercyclic. We considered the existing partial solutions due to Bernal-Gonz´alez [15] and B`es and Conejero [9] to develop our results. An illustrative example is also provided.