Hypercyclic operators that commute with the Bergman backward shift

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A new class of frequently hypercyclic operators (2010, background): “That the behaviour of the eigenvectors of an operator has an influence on its hypercyclicity properties was first discovered by Godefroy and Shapiro in [14]: their work deals with eigenvectors associated to eigenvalues of modulus strictly larger than 1 and strictly smaller than 1.”
Szemeredi's theorem, frequent hypercyclicity and multiple recurrence (2010, background): “For results along this direction we refer to (Bourdon and Shapiro, 2000).”
Invariant Gaussian measures for operators on Banach spaces and linear dynamics (2007, methodology): “This method, inspired by the works of Flytzanis [10, 11] and Bourdon and Shapiro [6], is applicable to operators on Hilbert spaces which have a sufficiently rich supply of eigenvectors associated to eigenvalues of modulus 1.”