Hypercyclic operators on non-locally convex spaces

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Lineability criteria, with applications (2013, background): “Perhaps one of the most outstanding is the HerreroBourdon theorem (see [43, 62]) asserting that the set HC(T ) of hypercyclic vectors of a (continuous, linear) operator T : X → X on a complex Banach space X is dense-lineable (moreover, the dense subspace obtained is T -invariant; the result was exte”
Linear subsets of nonlinear sets in topological vector spaces (2013, background): “In a chain of successive improvements, Herrero [185], Bourdon [114], Bès [87], and Wengenroth [270] demonstrated that if T is a hypercyclic operator on an arbitrary topological vector space X, then HC(T ) is dense-lineable.”
Hypercyclic behaviour of operators in a hypercyclic C 0 -semigroup (2007, background): “A continuous linear operator T : X → X on a topological vector space X is said to be hypercyclic if there is a vector x ∈ X (called a hypercyclic vector) whose orbit under T , Orb(T, x) := {T nx : n ∈ N}, is dense in X.”
On the spectrum of frequently hypercyclic operators (2008, methodology): “This obstacle was removed by Wengenroth [26], which allowed him to extend the Bourdon and Feldman theorem to arbitrary topological vector spaces, see also the survey [18].”
On dense-lineability of sets of functions on R (2009, background): “(In fact, any universal operator on any topological vector space admits a dense-linear manifold consisting, except for zero, of universal vectors; see [14].”