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On the lifting of bounded sets in Fréchet spaces

Published online by Cambridge University Press:  20 January 2009

José Bonet  and
Susanne Dierolf
José Bonet
Affiliation:
Universidad Politécnica de Valencia, Departamento de matématica Aplicada, E.T.S. Arquitectura, E-46071 Valencia, Spain
Susanne Dierolf
Affiliation:
FB Mathematik IV, Universität Trier, Postfach 3825, D-5500 Trier, Germany
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Abstract

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This paper considers the behaviour of a quotient map between Fréchet spaces concerning the lifting of bounded sets. The main result shows that a quotient map between Fréchet spaces that lifts bounded sets with closure (or equivalently such that its strong transpose is a topological isomorphism) must also lift bounded sets without closure.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 36 , Issue 2 , June 1993 , pp. 277 - 281
Copyright
Copyright © Edinburgh Mathematical Society 1993

References

REFERENCES

1.Bastin, F., Distinguishedness of weighted Fréchet spaces of continuous functions, Proc. Edinburgh Math. Soc. (2) 35 (1992), 271–283.CrossRefGoogle Scholar
2.Bierstedt, K. D., Meise, R. G. and Summers, W. H., Köthe sets and Köthe sequence spaces, in Funct. Anal., Holomorphy and Approx. Theory (North-Holland Math. Studies 71, Amsterdam 1982), 27–91.Google Scholar
3.Bonet, J. and Dierolf, S., On LB-spaces of Moscatelli type, Doga Mat. 13 (1989), 9–33.Google Scholar
4.Bonet, J. and Dierolf, S., Fréchet spaces of Moscatelli type, Rev. Mat. Univ. Complut. Madrid 2 (1989), 77–92.Google Scholar
5.Bonet, J., Dierolf, S. and Fernández, C., On the three-space-problem for distinguished Fréchet spaces, Bull. Soc. Roy. Sci. Liège 59 (1990), 301–306.Google Scholar
6.Bonet, J., Dierolf, S. and Fernández, C., The bidual of a distinguished Fréchet space need not be distinguished, Archiv Math. 57 (1991), 475–478.CrossRefGoogle Scholar
7.Cholodovskij, V. E., On quasinormability of semimetrizable topological vector spaces, Funkc. Anal. 7 (1976), 157–160.Google Scholar
8.De Wilde, M., Sur le relèvement des parties bornées d'un quotient d'espaces vectoriels topologiques, Bull. Soc. Roy. Sci. Liège 5–6 (1974), 299–301.Google Scholar
9.Díaz, J. C., A note on holomorphic functions of bounded type in Fréchet spaces, J. Math. Anal. Appl., to appear.Google Scholar
10.Grothendieck, A., Topological Vector Spaces (Gordon and Breach, New York 1973).Google Scholar
11.Jarchow, H., Locally Convex Spaces (B.G. Teubner, Stuttgart 1981).CrossRefGoogle Scholar
12.Köthe, G., Topological Vector Spaces I, II (Springer-Verlag, Heidelberg 1969, 1979).Google Scholar
13.Carreras, P. Pérez and Bonet, J., Barrelled Locally Convex Spaces (North-Holland Math. Studies 131, Amsterdam 1987).CrossRefGoogle Scholar