The strong disjoint blow-up/collapse property

Let x be a topological vector space,and let b (x) be the algebra of continuous linear operators on x. the operators t 1,.,t n ε b (x) are disjoint hypercyclic if there is x ε x such that the orbit { (t 1 n (x),.,t n n (x)): n ε n } is dense in x ×. × x. bès and peris have shown that if t 1,.,t n 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 t 1,.,t n 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. © 2013 héctor n. salas.