The role of the spectrum in the cyclic behavior of composition operators

By E. G. Gutiérrez, A. M. Rodríguez. 2004

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Linear subsets of nonlinear sets in topological vector spaces (2013, background): “In Shapiro’s book [255] it is proved that Cφ is hypercyclic on H p if and only if φ lacks fixed points in D; see [115] and [147] for extensions.”
Disjoint mixing operators (2012, methodology): “Analogue extensions were done to Seidel and Walsh’s [27] hypercyclicity result on non-Euclidean translations acting on the space H(D) of holomorphic functions on the unit disc: Bourdon and Shapiro [12] and Gallardo-Gutiérrez and Montes-Rodríguez [18] showed the existence of slow-growth universal fun”