Hypercyclic Translation Operators on the Algebra of Compact Operators

Disjoint linear dynamical properties of elementary operators

“…The equivalent conditions for densely d-hypercyclicity (or equivalently, disjoint topological transitivity) in Theorem 2.2 can be given for the situation where B 0 (H) is replaced by an arbitrary non-unital C * -algebra A, and the set of all finite rank orthogonal projections on H is replaced by the normalized canonical approximate unit in A. See [18,Remark 3] for some details.…”

“…In last decades, linear dynamical properties of operators have been studied in many research articles; see monographs [1,16], and recent papers [18,22]. J. Bès and A. Peris in 2007 [7] introduced and studied a new version of disjointness for hypercyclicity, topological transitivity and topological mixing properties regarding a finite sequence of operators on a Fréchet space.…”

“…In [21], the authors consider disjoint dynamics of weighted translations operators on a wide class of general Banach lattices, and give a characterization for weighted translation operators to be disjoint hypercyclic and topologically mixing on such Banach spaces. Recently, in [18] we have characterized hypercyclic elementary operators (studied in papers [8,13,14,15]) on the space of compact linear operators on a separable Hilbert space. Here, we will give some necessary and sufficient conditions for an elementary operator corresponding to unitary and invertible operators to be disjoint hypercyclic.…”

Hypercyclic Operators on Hilbert C*-modules

“…In last decades, linear dynamical properties of operators have been studied in many research articles; see monographs [3,28], and recent papers [50,47].…”

“…Recently, in [49] we have for instance characterized hypercyclic weighted composition operators on the commutative C * -algebra of continuous functions vanishing at infinity on a locally compact, non-compact Hausdorff space. Moreover, in [50] we have characterized hypercyclic elementary operators on the space of compact linear operators on a separable Hilbert space. The dynamics of some similar operators have been considered earlier such as conjugate operators, see [34], and left multiplication operators, see [54], [55], [56].…”