Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-28T14:49:36.502Z Has data issue: false hasContentIssue false
  • English
  • Français

On weighted inductive limits of spaces of Fréchet-valued continuous functions

Part of: Linear function spaces and their duals

Published online by Cambridge University Press:  09 April 2009

Antonio Galbis
Antonio Galbis
Affiliation:
Facultad de Matemáticas Universitat de ValènciaBurjasot (Valencia), Spain
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this article we continue the study of weighted inductive limits of spaces of Fréchet-valued continuous functions, concentrating on the problem of projective descriptions and the barrelledness of the corresponding “projective hull”. Our study is related to the work of Vogt on the study of pairs (E, F) of Fréchet spaces such that every continuous linear mapping from E into F is bounded and on the study of the functor Ext1 (E, F) for pairs (E, F) of Fréchet spaces.

MSC classification

Secondary: 46E40: Spaces of vector- and operator-valued functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 50 , Issue 2 , April 1991 , pp. 233 - 242
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Bellenot, S. and Dubinsky, E., ‘Fréchet spaces with nuclear Köthe quotients’, Trans. Amer. Math. Soc. 273 (1982), 579–594.Google Scholar
[2]Bierstedt, K. D., Meise, R. and Summers, W. H., ‘A projective description of weighted inductive limits’, Trans. Amer. Math. Soc. 272 (1982), 107–160.CrossRefGoogle Scholar
[3]Bierstedt, K. D., Meise, R. and Summers, W. H., ‘Köthe sets and Köthe sequence spaces’, in Functional analysis, holomorphy and approximation theory, pp. 27–91, (NorthHolland Math. Studies 71, Amsterdam, New York, and Oxford, 1982).Google Scholar
[4]Bierstedt, K. D. and Bonet, J., ‘Projective descriptions on weighted inductive limits. The vector valued cases’, in Advances in the theory of Fréchet spaces, edited by Terziouglu, D., pp. 195–221, (Reidel Co., NATO-ASI Series, Kluwer Acad. P.V.L., 1989).CrossRefGoogle Scholar
[5]Bonet, J., ‘On weighted inductive limits of spaces of continuous functions’, Math. Z. 192 (1986), 9–20.CrossRefGoogle Scholar
[6]Bonet, J., ‘Projective descriptions of inductive limits of Fréchet sequence spaces’, Arch. Math. 48 (1987), 331–336.CrossRefGoogle Scholar
[7]Bonet, J. and Galbis, A., ‘The identity L(E,F) = LB(E,F), tensor products and inductive limits’, to appear in Note Mat.Google Scholar
[8]Galbis, A., ‘Köthe sequences spaces with values in Fréchet or (DF)-spaces’, Bull. Soc. Roy. Sci. Liège 57 (1988), 157–172.Google Scholar
[9]Grothendieck, A., Topological vector spaces, (Gordon & Breach, New York, London and Paris, 1973).Google Scholar
[10]Jarchow, H., Locally convex spaces, (B. G. Teubner, Stuttgart, 1981).CrossRefGoogle Scholar
[11]Köthe, G., Topological vector spaces I and II, (Springer Verlag, Berlin, Heidelberg, and New York, 1969 and 1979).Google Scholar
[12]Krone, J. and Vogt, D., ‘The splitting relation for Köthe spaces’, Math. Z. 190 (1985), 387–400.CrossRefGoogle Scholar
[13]Carreras, P. Perez and Bonet, J., Barrelled locally convex spaces, (North-Holland Math. Studies 131, Amsterdam, New York, Oxford, 1987).Google Scholar
[14]Vogt, D., ‘Frécheträume, zwischen denen jede stetige lineare Abbildung beshränkt ist’, J. Reine Angew. Math. 345 (1983), 182–200.Google Scholar
[15]Vogt, D., ‘On the functor Ext1 (E, F) for Fréchet spaces’, Studia Math. 85 (1987), 163–197.CrossRefGoogle Scholar
[16]Vogt, D., ‘Some results on continuous linear maps between Fréchet spaces’, Functional analysis: Surveys and recent results III, pp. 349–381, (North-Holland Math. Studies 90 (1984).Google Scholar
[17]Vogt, D., ‘On two problems of Mityagin’, Math. Nachr. 141 (1989), 13–25.CrossRefGoogle Scholar
[18]Vogt, D., ‘On two classes of (F)-spaces’, Arch. Math. 45 (1985), 225–266.CrossRefGoogle Scholar
[19]Vogt, D., Lectures on Projective spectra of (DF)-spaces, Part I, (Lectures held in the Functional Analysis Seminar Düsseldorf/Wuppertal 1987).Google Scholar