A mixing operator $T$ for which $(T,T^2)$ is not disjoint transitive

Abstract

Using a result from ergodic Ramsey theory, we answer a question posed by Bès, Martin, Peris and Shkarin by showing a mixing operator $T$ on a Hilbert space such that the tuple $(T,T^2)$ is not disjoint transitive.

arXiv commentarXiv admin note: substantial text overlap with arXiv:1411.7721