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dc.creatorSwartz, Charles
dc.date2012-06-20
dc.identifierhttp://www.revistaproyecciones.cl/article/view/1150
dc.identifier10.4067/S0716-09172012000200004
dc.descriptionLet 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
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dc.languagespa
dc.publisherUniversidad Católica del Norte.es-ES
dc.relationhttp://www.revistaproyecciones.cl/article/view/1150/1133
dc.rightsDerechos de autor 2012 Proyecciones. Journal of Mathematicses-ES
dc.sourceProyecciones. Journal of Mathematics; Vol 31 No 2 (2012); 149-164en-US
dc.sourceProyecciones. Revista de Matemática; Vol. 31 Núm. 2 (2012); 149-164es-ES
dc.source0717-6279
dc.source0716-0917
dc.titleUniform Convergence and the Hahn-Schur Theoremes-ES
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/publishedVersion
dc.typeArtículo revisado por pareses-ES


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