Approximation of chaotic operators
In the present paper, Li-Yorke and distributionally chaotic linear operators on Hilbert spaces are studied. The closures and the interiors of the set of all Li-Yorke chaotic operators or all distributionally chaotic operators are discussed. The arcwise connectedness of these sets is proved. The authors also obtain the following relation between hypercyclic operators and distributionally chaotic operators: the set of all hypercyclic operators belongs to the closure of the set of all distributionally chaotic operators. The relation between norm-unimodal operators and distributionally chaotic operators is also obtained.
scientific article; zbMATH DE number 6045977