TY - JOUR
A2 - Fošner, Ajda
AU - Salas, Héctor N.
PY - 2013
DA - 2013/11/04
TI - The Strong Disjoint Blow-Up/Collapse Property
SP - 146517
VL - 2013
AB - Let X be a topological vector space, and let ℬ(X) be the algebra of continuous linear operators on X. The operators T1,…,TN∈ℬ(X) are disjoint hypercyclic if there is x∈X such that the orbit {(T1n(x),…,TNn(x)):n∈ℕ} is dense in X×…×X. Bès and Peris have shown that if T1,…,TN satisfy the Disjoint Blow-up/Collapse property, then they are disjoint hypercyclic. In a recent paper Bès, Martin, and Sanders, among other things, have characterized disjoint hypercyclic N-tuples of weighted shifts in terms of this property. We introduce the Strong Disjoint Blow-up/Collapse property and prove that if T1,…,TN satisfy this new property, then they have a dense linear manifold of disjoint hypercyclic vectors. This allows us to give a partial affirmative answer to one of their questions.
SN - 2314-8896
UR - https://doi.org/10.1155/2013/146517
DO - 10.1155/2013/146517
JF - Journal of Function Spaces and Applications
PB - Hindawi Publishing Corporation
KW -
ER -