Barrelledness conditions on S(Σ;E) and B(Σ;E).
| dc.contributor.author | Mendoza Casas, José | |
| dc.date.accessioned | 2023-06-21T02:02:33Z | |
| dc.date.available | 2023-06-21T02:02:33Z | |
| dc.date.issued | 1982 | |
| dc.description.abstract | Let Ω be a nonempty set, and let Σ be a field of subsets of Ω. If E is a locally convex space we denote by S(Σ;E) the vector space of all Σ-simple functions defined on Ω with values in E, and by B(Σ;E) the vector space of all functions defined on Ω with values in E which are uniform limits of Σ-simple functions. We give some results characterizing when the spaces S(Σ;E) and B(Σ;E) endowed with the uniform convergence topology are barrelled or infrabarrelled. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/16891 | |
| dc.identifier.doi | 10.1007/BF01456405 | |
| dc.identifier.issn | 0025-5831 | |
| dc.identifier.officialurl | http://www.springerlink.com/content/x35m3k7433761318/ | |
| dc.identifier.relatedurl | http://www.springerlink.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/64686 | |
| dc.issue.number | 1 | |
| dc.journal.title | Mathematische Annalen | |
| dc.language.iso | eng | |
| dc.page.final | 22 | |
| dc.page.initial | 11 | |
| dc.publisher | Springer | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.98 | |
| dc.subject.keyword | uniform convergence topology | |
| dc.subject.keyword | barrelled | |
| dc.subject.keyword | infrabarrelled | |
| dc.subject.keyword | uniform limit of vector valued simple functions | |
| dc.subject.ucm | Análisis funcional y teoría de operadores | |
| dc.title | Barrelledness conditions on S(Σ;E) and B(Σ;E). | |
| dc.type | journal article | |
| dc.volume.number | 261 | |
| dcterms.references | Diestel, J., Uhl, J.J., Jr.: Vector measures. Mathematical surveys. No. 15. Providence: American Mathematical Society 1977 Hollstein, R.: Über die Tonneliertheit von lokalkonvexen Tensorprodukten. Manuscripta Math.22, 7-12 (1977) Hollstein, R.: Permanence properties ofC(X;E) (to appear) Horváth, J.: Topological vector spaces and distributions. London, Amsterdam, Paris: Addison Wesley 1966 Köthe, G.: Topological vector spaces I. Berlin, Heidelberg, New York: Springer 1969 Marquina, A., Sanz Serna, J.M.: Barrelledness conditions onc o (E). Arch. Math.31 589-596 (1978) Mendoza, J.: Barrelledness onc o (E). Arch. Math. (to appear) Mendoza, J.: Necessary and sufficient conditions forC(X;E) to be barrelled or infrabarrelled. Simon Stevin (to appear) Mujica, J.: Spaces of continuous functions with values in an inductive limit (to appear) Pietsch, A.: Nuclear locally convex spaces. Berlin, Heidelberg, New York: Springer 1972 Schmets, J.: Espaces de fonctions continues. Lecture Notes in Mathematics. Vol. 519. Berlin, Heidelberg, New York: Springer 1976 Schmets, J.: An example of the barrelled space associated toC(X;E). Lecture Notes in Mathematics, Vol. 843, pp. 561-571. Berlin, Heidelberg, New York: Springer 1981 Shuchat, A.H.: Integral representation theorems in topological vector spaces. Trans. Am. Math. Soc.172, 373-397 (1972) Swong, K.: A representation theory of continuous linear maps. Math. Ann.155, 270-291 (1964) | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 3fdf00ed-ed02-482c-a736-bb87c2753a89 | |
| relation.isAuthorOfPublication.latestForDiscovery | 3fdf00ed-ed02-482c-a736-bb87c2753a89 |
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