On a Theorem of Godefroy and Shapiro

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Mixing operators and small subsets of the circle (2011, background): “oblem has received a lot of attention in the speciﬁc setting of linear dynamics, i.e. when the transformation T is a continuous linear operator acting on a topological vector space X ([25], [8], [7], [14], [28]). The main reason is that people working in linear dynamics are mostly interested in stud”
Lineability criteria, with applications (2013, background): “Bonilla and Grosse-Erdmann (see [37] and [38]) have proved that such a T satisfies the so-called Frequent Hypercyclicity Criterion, one of whose items is the existence of a dense subset D ⊂ X such that ∑ n≥1 T x converges unconditionally for every x ∈ D.”
Linear subsets of nonlinear sets in topological vector spaces (2013, background): “1, composition operators Cφ on H(D) with φ an automorphism without fixed points, nonscalar differential operators Φ(D) on H(C), and the Rolewicz operator λB with |λ| > 1 on c0 or p, 1 ≤ p < ∞, among others) are also frequently hypercyclic; see [47], [48], [103], and [104].”