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Journal of Function Spaces and Applications
Volume 2013 (2013), Article ID 146517, 6 pages
http://dx.doi.org/10.1155/2013/146517
Research Article

The Strong Disjoint Blow-Up/Collapse Property

Department of Mathematics, University of Puerto Rico, Mayagüez, PR 00681, USA

Received 9 May 2013; Revised 14 August 2013; Accepted 15 August 2013

Academic Editor: Ajda Fošner

Copyright © 2013 Héctor N. Salas. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be a topological vector space, and let be the algebra of continuous linear operators on . The operators are disjoint hypercyclic if there is such that the orbit is dense in . Bès and Peris have shown that if 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 -tuples of weighted shifts in terms of this property. We introduce the Strong Disjoint Blow-up/Collapse property and prove that if 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.