Hostname: page-component-8448b6f56d-xtgtn Total loading time: 0 Render date: 2024-04-24T08:38:34.702Z Has data issue: false hasContentIssue false

Answer to a Question of S. Rolewicz

Published online by Cambridge University Press:  20 November 2018

Félix Cabello Sánchez
Affiliation:
Departamento de Matemáticas, Universidad de Extremadura, Avenida de Elvas, 06071 Badajoz, España, e-mail: fcabello@unex.escastillo@unex.es
Jesús M. F. Castillo
Affiliation:
Departamento de Matemáticas, Universidad de Extremadura, Avenida de Elvas, 06071 Badajoz, España, e-mail: fcabello@unex.escastillo@unex.es
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.

We exhibit examples of $F$-spaces with trivial dual which are isomorphic to its quotient by a line, thus solving a problem in Rolewicz's Metric Linear Spaces.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2003

References

[1] Cabello Sánchez, F. and Castillo, J. M. F., The long homology sequence for quasi-Banach spaces, with applications. Positivity, to appear.Google Scholar
[2] Hilton, E. and Stammbach, K., A course in homological algebra. Graduate Texts in Math. 4, Springer-Verlag, 1970.Google Scholar
[3] Kalton, N., Peck, N. T. and Roberts, W., An F-space sampler. LondonMath. Soc. Lecture Note Series 89, Cambridge University Press, 1984.Google Scholar
[4] Peck, N. T. and Starbird, T., L0 is ω-transitive. Proc. Amer.Math. Soc. 283 (1981), 700704.Google Scholar
[5] Ribe, M., Examples for the nonlocally convex three space problem. Proc. Amer.Math. Soc. 237 (1979), 351355.Google Scholar
[6] Rolewicz, S., Metric Linear Spaces. D. Reidel Publishing Company and PWN. Polish Scientific Publishers, 1984.Google Scholar