With cedram.org
Table of contents for this issue | Previous article | Next article
Gilles Godefroy
Espaces de Banach : existence et unicité de certains préduaux
Annales de l'institut Fourier, 28 no. 3 (1978), p. 87-105, doi: 10.5802/aif.702
Article PDF | Reviews MR 81i:46015 | Zbl 0368.46015 | 1 citation in Cedram

Résumé - Abstract

We study in this work the following problem: given a Banach space $E$, does there exist a Banach space $X$ such that $X^{\prime }$ be isometric to $E$? We give an existence criterion of such a space $X$ for a particular type of space $E$. We prove that such a space $X$ is unique, up to an isometry, for some classes of spaces $E$. We then deduce some results about isometries of certain Banach spaces and geometry of certain compact convex sets.


[1] E. ODELL and H.P. ROSENTHAL, A double dual characterization of separable Banach spaces containing l1, Israel J. of Math., 20 (1975), 375-384.  MR 51 #13654 |  Zbl 0312.46031
[2] R.E. JAMISON, R.C. O'BRIEN et P.D. TAYLOR, On embedding a compact convex set into a locally convex space, Queen's Mathematics Preprint 1974-18, Queen's University, Kingston, Ontario, Canada.  Zbl 0325.46003