Explicit Constructions of Dense Common Hypercyclic Subspaces

Abstract

We give an explicit construction of a dense infinite dimensional vector space of hypercyclic vectors for the weighted backward shift Tλ (|λ| > 1). We also develop a technique to construct common hypercyclic vectors for countable families of these operators. The techniques developed here do not rely on the Baire category theorem or any kind of existence proof, as do most approaches to this problem.