Weighted shifts and disjoint hypercyclicity

Disjoint Li-Yorke Chaos in Frechet Spaces ´ M. Kostic

“…Finally, we want to note that these operators cannot be d-hypercyclic due to [37, Theorem 2.1] (cf. also [9] and [11] for basic results given in this direction). Now we will provide an application of Corollary 3.2 to unbounded unilateral backward shift operators: Example 3.5.…”

A note on the hypercyclicity of operator-weighted shifts

“…, T r ) is d-mixing. Bès, Martin, and Sanders [5] studied the disjoint hypercyclicity of unilateral and bilateral weighted shift operators. In addition, Hazarika and Arora [9] characterized the hypercyclicity of the bilateral operator-weighted shift T on L 2 (K) with weight sequence {A n } ∞ n=−∞ of positive invertible diagonal operators on a separable complex Hilbert space K. Inspired by Hazarika and Arora's work, Liang and Zhou [11] discussed the supercyclicity and hereditarily hypercyclicity of operator-weighted shifts.…”

Disjoint hypercyclic powers of weighted translations on groups

“…For example, disjoint hypercyclicity was studied in [2], [3], [4], [16], [17]. Besides, disjoint hypercyclic and supercyclic powers of weighted backward shifts were also characterized in [5], [6], [15]. Recently, hypercyclic, supercyclic and chaotic weighted translations on locally compact groups and their homogeneous spaces were characterized in [8], [9], [7].…”