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A barrelledness criterion for C0(E)

Mendoza Casas, José (1993) A barrelledness criterion for C0(E). Archiv der Mathematik, 40 (1). pp. 156-158. ISSN 0003-889X

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Abstract

Denote by C0(E) the linear space of all sequences in E which converge to zero in E endowed with its natural topology. A. Marquina and J. M. Sanz Serna [same journal 31 (1978/79), 589–596; MR0531574 (80i:46010)] gave necessary and sufficient conditions to ensure the quasibarrelledness of C0(E), namely: (i) E is quasibarrelled and (ii) the strong dual of E satisfies condition (B) of Pietsch. Moreover, if E is complete in the sense of Mackey, (i) and (ii) characterize the barrelledness of C0(E). Even in the absence of completeness in the sense of Mackey, the last result is true as the article under review shows by a clever use of a "sliding-hump'' technique. Interesting consequences of those results in the theory of tensor products and spaces of vector-valued continuous functions can be found in a recent paper by A. Defant and W. Govaerts ["Tensor products and spaces of vector-valued continuous functions'', Manuscripta Math., to appear] and in the monograph of J. Schmets [Spaces of vector-valued continuous functions, Lecture Notes in Math., 1003, Springer, Berlin, 1983].


Item Type:Article
Uncontrolled Keywords:barrelledness
Subjects:Sciences > Mathematics > Topology
ID Code:16889
References:

A. Marquina andJ. M. Sanz Serna,Barrelledness conditions onC 0(E). Arch. Math.31, 589-596 (1978).

J.Mentdoza, Necessary and sufficient conditions forC(X; E) to be barrelled or infrabarrelled (to appear in Simon Stevin).

A.Pietsch, Nuclear Locally Convex Spaces. Berlin 1972.

Deposited On:26 Oct 2012 08:25
Last Modified:13 Nov 2013 16:22

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