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Barrelledness conditions on S(Σ;E) and B(Σ;E).

Mendoza Casas, José (1982) Barrelledness conditions on S(Σ;E) and B(Σ;E). Mathematische Annalen, 261 (1). pp. 11-22. ISSN 0025-5831

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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.

Item Type:Article
Uncontrolled Keywords:uniform convergence topology; barrelled; infrabarrelled; uniform limit of vector valued simple functions
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:16891
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)

Deposited On:26 Oct 2012 08:21
Last Modified:13 Nov 2013 16:25

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