The Strong Disjoint Blow-Up/Collapse Property
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...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/146517 |
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| _version_ | 1832562666441277440 |
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| author | Héctor N. Salas |
| author_facet | Héctor N. Salas |
| author_sort | Héctor N. Salas |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-42e2a3722db64f49a2b0dd31a2f50a07 |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-42e2a3722db64f49a2b0dd31a2f50a072025-02-03T01:22:00ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/146517146517The Strong Disjoint Blow-Up/Collapse PropertyHéctor N. Salas0Department of Mathematics, University of Puerto Rico, Mayagüez, PR 00681, USALet 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.http://dx.doi.org/10.1155/2013/146517 |
| spellingShingle | Héctor N. Salas The Strong Disjoint Blow-Up/Collapse Property Journal of Function Spaces and Applications |
| title | The Strong Disjoint Blow-Up/Collapse Property |
| title_full | The Strong Disjoint Blow-Up/Collapse Property |
| title_fullStr | The Strong Disjoint Blow-Up/Collapse Property |
| title_full_unstemmed | The Strong Disjoint Blow-Up/Collapse Property |
| title_short | The Strong Disjoint Blow-Up/Collapse Property |
| title_sort | strong disjoint blow up collapse property |
| url | http://dx.doi.org/10.1155/2013/146517 |
| work_keys_str_mv | AT hectornsalas thestrongdisjointblowupcollapseproperty AT hectornsalas strongdisjointblowupcollapseproperty |