Topological Transitivity for Sequences of Operators on the $$C^*$$ C ∗ -Algebra-Valued Lebesgue Spaces

Hypercyclic Operators on Hilbert C*-modules

“…Specially, hypercyclic weighted shifts on ℓ p (Z) were characterized in [37,26], and then C-C. Chen and C-H. Chu, using aperiodic elements of locally compact groups, extended the results in [37] to weighted translations on Lebesgue spaces in the context of a second countable group [19]. Afterwards, many other linear dynamics in connection with this theme have been studied; see [13,14,22,23,24].…”

Hypercyclic sequences of weighted translations on hypergroups

“…For instance, the existence of hypercyclic weighted translations on L p (G) was studied in [12]. See also [10,11] for the hypergroup case and vectorvalued version. In [1,9] some linear dynamical properties of weighted translation operators on Orlicz spaces in the context of locally compact groups have been studied.…”

Dynamics of weighted translations generated by group actions

“…Also, the existence of hypercyclic weighted translations on L p (G) was discussed in [15]. We refer to papers [13,14] for readers interested in the hypergroup case and vector-valued version. Besides, linear dynamics for weighted translations on the Orlicz space L Φ (G) were first investigated by [2,12] where Φ is a Young function.…”