Disjoint hypercyclicity of weighted composition operators

Disjoint distributional chaos in Fréchet spaces

“…Suppose that there exist an infinite set S of natural numbers such that the series n∈S b n e n converges in X, and that the upper density of set It is beyond the scope of this paper to extend the assertions of [28,Theorem 4.8(c)] and [11,Corollary 28], provided that (e n ) n∈N is an unconditional basis of X (concerning these and previously stated results, we want only to stress that similar statements hold for bilateral backward shifts (see [11,Theorem 29,Theorem 30,Corollary 31]), while the same comment and problem can be posed for [11,Corollary 32]). The interested reader might be also interested in the analysis of disjoint distributionally chaotic properties of composition operators (see [11], the doctoral dissertation of Ö. Martin [43], the paper [33] by Z. Kamali, B. Yousefi and references cited therein for more details about this subject) and reconsideration of structural results from the paper [26] by F. Martínez-Giménez, P. Oprocha and A. Peris for disjoint distributional chaos.…”

“…For more details about disjoint hypercyclic operators and their generalizations, one may refer e.g. to [14], [16]- [17], [33], [35]- [36], [41], [43]- [44], [51]- [53], [56] and references cited therein.…”