Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-23T03:03:42.387Z Has data issue: false hasContentIssue false

Closed linear maps from a barrelled normed space into itself need not be continuous

Published online by Cambridge University Press:  17 April 2009

José Bonet
Affiliation:
Departamento de Matemática AplicadaE.T.S. ArquitecturaUniversidad Politécnica de ValenciaE-46071 ValenciaSpain e-mail: [email protected]
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.

Examples of normed barrelled spaces E or quasicomplete barrelled spaces E are given such that there is a non-continuous linear map from the space E into itself with closed graph.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]Amemiya, I. and Komura, Y., ‘Über nichtvollständige Montelräume’, Math. Ann. 177 (1968), 273277.CrossRefGoogle Scholar
[2]Dodds, P.G. and Ricker, W.J., ‘Spectral measures and the Bade reflexivity theorem’, J. Funct. Anal. 61 (1985), 136163.CrossRefGoogle Scholar
[3]Köthe, G., Topological vector spaces II (Springer-Verlag, Berlin, Hemidelberg, New York, 1979).CrossRefGoogle Scholar
[4]Okada, S. and Ricker, W.J., ‘Continuous extensions of spectral measures’, Colloq. Math. 71 (1996), 115132.CrossRefGoogle Scholar
[5]Okada, S. and Ricker, W.J., ‘Spectral measures and automatic continuity’, Bull. Belg. Math. Soc. 3 (1996), 267279.Google Scholar
[6]Okada, S. and Ricker, W.J., ‘Integration with respect to the canonical spectral measure in sequence spaces’, (Preprint, Johannes Kepler Universität Linz, 1997).Google Scholar
[7]Carreras, P. Pérez and Bonet, J., Barrelled locally convex spaces, North-Holland Math. Studies 131 (North-Holland, Amsterdam, 1987).CrossRefGoogle Scholar