| dc.creator | Swartz, Charles | |
| dc.date | 2017-05-22 | |
| dc.identifier | http://www.revistaproyecciones.cl/article/view/1572 | |
| dc.identifier | 10.4067/S0716-09172004000100005 | |
| dc.description | Let X, Y be locally convex spaces and L(X, Y ) the space of continuous linear operators from X into Y . We consider 2 types of multiplier convergent theorems for a series ∑ Tₕ in L(X, Y ). First, if λ is a scalar sequence space, we say that the series ∑ Tₕ is λ multiplier P convergent for a locally convex topology τ on L(X, Y ) if the series ∑ tₕTₕ is τ convergent for every t = {tₕ} ∈ λ. We establish conditions on λ which guarantee that a λ multiplier convergent series in the weak or strong operator topology is λ multiplier convergent in the topology of uniform convergence on the bounded subsets of X. Second, we consider vector valued multipliers. If E is a sequence space of X valued sequences, the series ∑ Tₕ is E multiplier convergent in a locally convex topology η on Y if the series ∑ Tₕxₕ is η convergent for every x = {xₕ} ∈ E. We consider a gliding hump property on E which guarantees that a series ∑ Tₕ which is E multiplier convergent for the weak topology of Y is E multiplier convergent for the strong topology of Y . | es-ES |
| dc.language | en | |
| dc.publisher | Universidad Católica del Norte. | es-ES |
| dc.rights | Derechos de autor 2004 Proyecciones. Journal of Mathematics | es-ES |
| dc.source | Proyecciones. Journal of Mathematics; Vol 23 No 1 (2004); 61-72 | en-US |
| dc.source | Proyecciones. Revista de Matemática; Vol. 23 Núm. 1 (2004); 61-72 | es-ES |
| dc.source | 0717-6279 | |
| dc.source | 0716-0917 | |
| dc.title | Orlicz-Pettis theorems for multiplier convergent operator valued series | es-ES |
| dc.type | info:eu-repo/semantics/article | |
| dc.type | info:eu-repo/semantics/publishedVersion | |
| dc.type | Artículo revisado por pares | es-ES |
