dc.creator | Swartz, Charles | |
dc.date | 2012-06-20 | |
dc.identifier | http://www.revistaproyecciones.cl/article/view/1150 | |
dc.identifier | 10.4067/S0716-09172012000200004 | |
dc.description | Let E be a vector space, F aset, G be a locally convex space, b : E X F — G a map such that ò(-,y): E — G is linear for every y G F; we write b(x, y) = x · y for brevity. Let λ be a scalar sequence space and w(E,F) the weakest topology on E such that the linear maps b(-,y): E — G are continuous for all y G F .A series Xj in X is λ multiplier convergent with respect to w(E, F) if for each t = {tj} G λ ,the series Xj=! tj Xj is w(E,F) convergent in E. For multiplier spaces λ satisfying certain gliding hump properties we establish the following uniform convergence result: Suppose j XX ij is λ multiplier convergent with respect to w(E, F) for each i G N and for each t G λ the set {Xj=! tj Xj : i} is uniformly bounded on any subset B C F such that {x · y : y G B} is bounded for x G E.Then for each t G λ the series ^jjLi tj xj · y converge uniformly for y G B,i G N. This result is used to prove a Hahn-Schur Theorem for series such that lim¿ Xj=! tj xj · y exists for t G λ,y G F. Applications of these abstract results are given to spaces of linear operators, vector spaces in duality, spaces of continuous functions and spaces with Schauder bases. | es-ES |
dc.format | application/pdf | |
dc.language | spa | |
dc.publisher | Universidad Católica del Norte. | es-ES |
dc.relation | http://www.revistaproyecciones.cl/article/view/1150/1133 | |
dc.rights | Derechos de autor 2012 Proyecciones. Journal of Mathematics | es-ES |
dc.source | Proyecciones. Journal of Mathematics; Vol 31 No 2 (2012); 149-164 | en-US |
dc.source | Proyecciones. Revista de Matemática; Vol. 31 Núm. 2 (2012); 149-164 | es-ES |
dc.source | 0717-6279 | |
dc.source | 0716-0917 | |
dc.title | Uniform Convergence and the Hahn-Schur Theorem | es-ES |
dc.type | info:eu-repo/semantics/article | |
dc.type | info:eu-repo/semantics/publishedVersion | |
dc.type | Artículo revisado por pares | es-ES |