Hypercyclic and chaotic weighted shifts

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Hypercyclic, mixing, and chaotic C0-semigroups induced by semiflows (2007, methodology): “Taking into account the characterizations of chaoticity for the left translation semigroup on L p ρ (I ) given in [12, 13], and the characterization of chaoticity for weighted shifts given in [11], one might guess that a summability condition will enter.”
Distributional chaos for operators with full scrambled sets (2013, unknown): “, Theorem 2 in [9]).”
Recurrence properties of hypercyclic operators (2014, background): “This characterization of A-hypercyclic weighted shifts complements the characterization of hypercyclic weighted shifts [16,22] and the recent characterization of frequently hypercyclic weighted shifts on p and c0 [6].”
Hypercyclic subspaces and weighted shifts (2012, background): “Such a sequence exists because every hypercyclic weighted shift is weakly mixing (see [6]).”
Linear chaos and frequent hypercyclicity (2014, background): “A characterization of chaotic weighted shifts is also known [26,30].”