# On the Hypercyclicity Criterion for operators of Read's type

## TL;DR

This paper proves that operators of Read's type on separable Banach spaces satisfy the Hypercyclicity Criterion, specifically showing that their direct sum with themselves is hypercyclic, advancing understanding of their dynamic properties.

## Contribution

It establishes that operators of Read's type inherently satisfy the Hypercyclicity Criterion by demonstrating their direct sum is hypercyclic, a novel insight into their structure.

## Key findings

- Operators of Read's type have no non-trivial invariant subsets.
- The direct sum of such an operator with itself is hypercyclic.
- Operators of Read's type satisfy the Hypercyclicity Criterion.

## 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.