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Duals of Banach spaces which admit nontrivial smooth functions

  • K. John (a1) and V. Zizler (a2)

Abstract

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).

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References

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[1]Amir, D. and Lindenstrauss, J., “The structure of weakly compact sets in Banach spaces”, Am. of Math. (2) 88 (1968), 3546.
[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).
[3]Leduc, Michel, “Densité de certaines families d'hyperplans tangents”, C.R. Acad. Sci. Paris Sér. A 270 (1970), 326328.
[4]Tacon, D.C., “The conjugate of a smooth Banach space”, Bull. Austral. Math. Soc. 2 (1970), 415425.
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Duals of Banach spaces which admit nontrivial smooth functions

  • K. John (a1) and V. Zizler (a2)

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