On the Hypercyclicity Criterion for operators of Read's type

Abstract

Let $T$ be a so-called operator of Read's type on a (real or complex) separable Banach space, having no non-trivial invariant subset. We prove in this note that $T\oplus T$ is then hypercyclic, i.e. that $T$ satisfies the Hypercyclicity Criterion.

8 pages; to appear in the special volume "The Mathematical Legacy of Victor Lomonosov" (de Gruyter)