Prǎjiturǎ's orbit-growth conjecture for Banach-space operators

Let $R$ be an operator on a Banach space, and define

$$A_R=\{x: \|R^t x\|\to\infty\}.$$

Prǎjiturǎ's conjecture. $A_R$ is either empty or dense.

The paper states that this conjecture was recently solved negatively by Hájek and Smith, so it is refuted. The source does not give the full bibliographic details of those references.