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A barrelledness criterion for C0(E)

Impacto

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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Resumen

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].


Tipo de documento:Artículo
Palabras clave:barrelledness
Materias:Ciencias > Matemáticas > Topología
Código ID:16889
Referencias:

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.

Depositado:26 Oct 2012 08:25
Última Modificación:13 Nov 2013 16:22

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