Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-13T05:56:11.562Z Has data issue: false hasContentIssue false

On the Duals of Flat Banach Spaces

Published online by Cambridge University Press:  20 November 2018

Abraham Bick*
Affiliation:
The Hebrew University, Jerusalem
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 give a simpler proof to a theorem of L. A. Karlovitz that the dual of a flat Banach space is flat, and also study some geometric properties of the dual space.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Day, M. M., Normed linear spaces 3rd. Ed. Springer-Verlang 1973.Google Scholar
2. Harrel, R. E. and Karlovitz, L. A., Girths and fiat Banach spaces, Bull. Amer. Math. Soc. 76 (1970) 1288-1291.Google Scholar
3. Harrel, R. E. and Karlovitz, L. A., The geometry of flat Banach spaces. Trans. Amer. Math. Soc. 192 (1974) 209-218.Google Scholar
4. Harrel, R. E. and Karlovitz, L. A., Flat and completely flat Banach spaces, University of Maryland Technical Note BN-714, 1971.Google Scholar
5. Karlovitz, L. A., On the duals of flat Banach spaces, Math. Ann. 202 (1973) 245-250.Google Scholar
6. Katzenelson, Y., An introduction to Harmonic Analysis, Wiley 1968.Google Scholar
7. Schaffer, J. J., Inner diameter, perimeter and girth of spheres, Math. Ann. 173 (1967) 59-79.Google Scholar