Hypercyclic operators on Banach spaces

By N. Clements. 2012

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A new class of frequently hypercyclic operators (2010, background): “Thus, although every infinite-dimensional separable Banach space supports a hypercyclic operator ([1],[8]), there are spaces on which there are no frequently hypercyclic operators.”
Disjoint mixing operators (2012, background): “With respect to the second theme, it is well known that every separable, infinite-dimensional Fréchet space X supports a hypercyclic operator T , thanks to the works of Ansari [1], BernalGonzález [5], and Bonet and Peris [11].”
Li–Yorke chaos in linear dynamics (2014, background): “Does dense Li–Yorke chaos imply the existence of a dense irregular manifold for operators on Fréchet (or Banach) spaces? It is well known that every infinite-dimensional separable Fréchet space supports a hypercyclic operator [1, 6, 9].”
Linear subsets of nonlinear sets in topological vector spaces (2013, methodology): “More precisely, in [84] Bernal-González and Ordóñez-Cabrera provided a series of conditions on a measure space (Ω,Σ, μ) to ensure the spaceability of the sets Lp(Ω)\ ⋃ q∈[1,p) Lq(Ω), Lp(Ω)\ ⋃ q∈[p,∞) Lq(Ω), and Lp(Ω) \ ⋃ q∈[1,∞)\{p} Lq(μ,X) (for p ≥ 1); whereas in [111] Botelho, Fávaro, Pellegri”