| dc.creator | Swartz, Charles | |
| dc.date | 2017-05-22 | |
| dc.identifier | https://www.revistaproyecciones.cl/index.php/proyecciones/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 ? T? in L(X, Y ). First, if ? is a scalar sequence space, we say that the series ? T? is ? multiplier P convergent for a locally convex topology ? on L(X, Y ) if the series ? t?T? is ? convergent for every t = {t?} ? ?. We establish conditions on ? which guarantee that a ? multiplier convergent series in the weak or strong operator topology is ? 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 ? T? is E multiplier convergent in a locally convex topology ? on Y if the series ? T?x? is ? convergent for every x = {x?} ? E. We consider a gliding hump property on E which guarantees that a series ? T? which is E multiplier convergent for the weak topology of Y is E multiplier convergent for the strong topology of Y . | es-ES |
| dc.publisher | Universidad Católica del Norte. | en-US |
| dc.rights | Copyright (c) 2004 Proyecciones. Journal of Mathematics | en-US |
| dc.source | Proyecciones (Antofagasta, On line); 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.subject | Locally convex spaces | es-ES |
| dc.subject | Orlicz-Pettis theorems | es-ES |
| dc.subject | continuous linear operators | es-ES |
| dc.subject | convergence | es-ES |
| dc.subject | scalar spaces | es-ES |
| dc.subject | sequence spaces | es-ES |
| dc.subject | series | es-ES |
| dc.subject | locally convex topology | es-ES |
| dc.subject | espacios localmente convexos | es-ES |
| dc.subject | teoremas de Orlicz-Pettis | es-ES |
| dc.subject | operadores lineales continuos | es-ES |
| dc.subject | convergencia. | es-ES |
| 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 | Peer-reviewed Article | en-US |
