Juan Bès

Chaotic unbounded differentiation operators

We construct dense sets of hypercyclic vectors for unbounded differention operators, including differentiation operators on the Hardy spaceH2, and the Laplacian operator onL2((Ω), for any bounded open subset Ω of ℝ2. Furthermore, we show that these operators are chaotic, in the sense of Devaney.

Approximation by chaotic operators and by conjugate classes

We show that every bounded linear operator on a separable, infinite-dimensional Hilbert space H is the sum of two operators in the norm-closure of the set of operators on H that are chaotic in the sense of Devaney. We also observe that the density of several classes of cyclic operators, with respect to the strong operator topology, may be derived from a result by Hadwin et al. (Proc Amer. Math. Soc. 76 (1979) 250–252).