Hypercyclic subspaces of a Banach space

Hypercyclicity in omega

“…Chan initiated in [8] the study of hypercyclitity for left-multipliers; his results in [8] are restricted to the Hilbert space setting. Later he pursued his work in [9], together with Taylor, by extending the study to Banach spaces. They obtained essentially the analogue of Proposition 2 for Banach spaces; see [9,Corollary 6].…”

“…Later he pursued his work in [9], together with Taylor, by extending the study to Banach spaces. They obtained essentially the analogue of Proposition 2 for Banach spaces; see [9,Corollary 6].…”

q-Frequent hypercyclicity in spaces of operators

“…Chan and R. Taylor [8], F. Martinez-Gimenez and A. Peris [17] and H. Petersson [19]. Indeed, left multiplication operators L R (S) = RS were considered in [3], [7], [8] and [17] and their general form C R,T (S) = RST was studied in [19]. A collective work in [3], [7] and [8] states that a bounded operator R on a separable Banach space X satisfies the Hypercyclicity Criterion if and only if the left multiplication operator L R is hypercyclic on L(X) in the topology of pointwise convergence.…”

“…Chan and R. Taylor [8], F. Martinez-Gimenez and A. Peris [17] and H. Petersson [19]. Indeed, left multiplication operators L R (S) = RS were considered in [3], [7], [8] and [17] and their general form C R,T (S) = RST was studied in [19].…”

“…Indeed, left multiplication operators L R (S) = RS were considered in [3], [7], [8] and [17] and their general form C R,T (S) = RST was studied in [19]. A collective work in [3], [7] and [8] states that a bounded operator R on a separable Banach space X satisfies the Hypercyclicity Criterion if and only if the left multiplication operator L R is hypercyclic on L(X) in the topology of pointwise convergence. This result holds for the topology of uniform convergence on compact subsets if X * is separable and X has the approximation property, see [3].…”