This is an announcement for the paper "Banach spaces which embed into their dual" by V.Capraro and S.Rossi.

Abstract: We provide a nice characterization of the classical Riesz-Frechet representation theorem: if a Banach space embeds isometrically into its dual space, under some other natural assumptions, then it is a Hilbert space and the embedding is actually the canonical one (which becomes automatically surjective). We also see that requiring surjectivity a priori, one can considerably weak one of the ''other hypothesis''. Anyway, it should remains to prove that our assumptions are minimal. It seems to be a difficult problem in general, because it is already not easy at all to find non-trivial examples (Hilbert spaces!) of Banach spaces which embed isometrically into their own dual. We will discuss in some details only the fatality of the ''isometric hypothesi'' which however brought us to find an example of compact convex Hausdorff space which does not admit a Borel measure with full support.

Archive classification: math.FA

Remarks: 7 pages

The source file(s), articolo.tex: 17079 bytes, is(are) stored in gzipped form as 0907.1813.gz with size 6kb. The corresponding postcript file has gzipped size 50kb.

Submitted from: capraro@mat.uniroma2.it

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