| dc.creator | Swartz, Charles | es |
| dc.date | 2012-06-20 | |
| dc.date.accessioned | 2025-03-31T13:12:20Z | |
| dc.date.available | 2025-03-31T13:12:20Z | |
| dc.identifier | https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/1150 | |
| dc.identifier | 10.4067/S0716-09172012000200004 | |
| dc.identifier.uri | https://revistaschilenas.uchile.cl/handle/2250/250934 | |
| 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 b(·,y): E → G is linear for every y ∈ 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 ∈ F .A series ΣjXj in X is λ multiplier convergent with respect to w(E, F) if for each t = {tj} ∈ λ ,the series Σj=1∞ tjxj is w(E,F) convergent in E. For multiplier spaces λ satisfying certain gliding hump properties we establish the following uniform convergence result: Suppose Σjxij is λ multiplier convergent with respect to w(E, F) for each i ∈ N and for each t ∈ λ the set {Σj=1∞ tjxij : i} is uniformly bounded on any subset B C F such that {x · y : y ∈ B} is bounded for x ∈ E.Then for each t ∈ λ the series Σj=1∞ tjxij · y converge uniformly for y ∈ B,i ∈ N. This result is used to prove a Hahn-Schur Theorem for series such that limi Σj=1∞ tjxij · y exists for t ∈ λ,y ∈ 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 |
| dc.format | application/pdf | |
| dc.language | spa | |
| dc.publisher | Universidad Católica del Norte. | en |
| dc.relation | https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/1150/1133 | |
| dc.rights | Copyright (c) 2012 Proyecciones. Journal of Mathematics | en |
| dc.source | Proyecciones (Antofagasta, On line); Vol. 31 No. 2 (2012); 149-164 | en |
| dc.source | Proyecciones. Revista de Matemática; Vol. 31 Núm. 2 (2012); 149-164 | es |
| dc.source | 0717-6279 | |
| dc.title | Uniform Convergence and the Hahn-Schur Theorem | es |
| dc.type | info:eu-repo/semantics/article | |
| dc.type | info:eu-repo/semantics/publishedVersion | |
