| dc.creator | Swartz, Charles | |
| dc.date | 2017-04-24 | |
| dc.identifier | https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/1488 | |
| dc.identifier | 10.4067/S0716-09172003000200004 | |
| 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 PTk in L(X, Y ). First, if ? is a scalar sequence space, we say that the series PTk is ? multiplier P convergent for a locally convex topology ? on L(X, Y ) if the series tkTk is ? convergent for every t = {tk} ? ?. 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 PTk is E multiplier convergent in a locally convex topology ? on Y if the series PTkxk is ? convergent for every x = {xk} ? E. We consider a gliding hump property on E which guarantees that a series PTk which is E multiplier convergent for the weak topology of Y is E multiplier convergent for the strong topology of Y. | es-ES |
| dc.format | application/pdf | |
| dc.language | spa | |
| dc.publisher | Universidad Católica del Norte. | en-US |
| dc.relation | https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/1488/1267 | |
| dc.rights | Copyright (c) 2003 Proyecciones. Journal of Mathematics | en-US |
| dc.source | Proyecciones (Antofagasta, On line); Vol. 22 No. 2 (2003); 135-144 | en-US |
| dc.source | Proyecciones. Revista de Matemática; Vol. 22 Núm. 2 (2003); 135-144 | es-ES |
| dc.source | 0717-6279 | |
| 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 |
