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

preprint2016arXivOpen access

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.

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

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A mixing operator TTT for which (T,T2)(T, T^2)(T,T2) is not disjoint transitive

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