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We prove that a continuous linear operator $T$ on a topological vector space$X$ with weak topology is mixing if and only if the dual operator $T'$ has nofinite dimensional invariant subspaces. This result implies thecharacterization of hypercyclic operators on the space $\omega$ due to Herzogand Lemmert and implies the result of Bayart and Matheron, who proved that forany hypercyclic operator $T$ on $\omega$, $T\oplus T$ is also hypercyclic.

Mixing operators on spaces with weak topology