Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-23T02:32:17.593Z Has data issue: false hasContentIssue false
  • English
  • Français

Duals of Banach spaces which admit nontrivial smooth functions

Published online by Cambridge University Press:  17 April 2009

K. John  and
V. Zizler
K. John
Affiliation:
Mathematical Institute, Czechoslovak Academy of Sciences, Praha;
V. Zizler
Affiliation:
Department of Mathematics, Charles University, Praha, Czechoslovakia.
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.

If a Banach space X admits a continuously Fréchet differentiable function with bounded nonempty support, then X* admits a projectional resolution of identity and a continuous linear one-to-one map into co(Γ).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 11 , Issue 2 , October 1974 , pp. 161 - 166
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Amir, D. and Lindenstrauss, J., “The structure of weakly compact sets in Banach spaces”, Am. of Math. (2) 88 (1968), 35–46.CrossRefGoogle Scholar
[2]Leduc, Michel, “Jauges différentiables et partitions de l'unité”, Séminaire Choquet, Initiation l'analyse, 4e année, 1964/65, 12–01 – 12–10 (Mathematica Seminosa, 1. Secrétariat Mathématique, Paris, 1965).Google Scholar
[3]Leduc, Michel, “Densité de certaines families d'hyperplans tangents”, C.R. Acad. Sci. Paris Sér. A 270 (1970), 326–328.Google Scholar
[4]Tacon, D.C., “The conjugate of a smooth Banach space”, Bull. Austral. Math. Soc. 2 (1970), 415–425.CrossRefGoogle Scholar