Correction to “On some subspaces of Banach spaces whose duals are $L_1$ spaces”
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Abstract:
E. Casini, E. Miglierina, L. Piasecki, and L. Veselý have recently constructed an example of an $L_{1}$-predual hyperplane $W$ of $c$ which does not contain a subspace isometric to $c$, in spite of the fact that the closed unit ball of $W$ contains an extreme point. This example shows that Remark A of Section 4 of [Proc. Amer. Math. Soc. 23 (1969), pp. 378-385], titled as above, is false. The purpose of this note is to present two correct versions of that Remark A and a short proof of our 1969 main result.References
- Emanuele Casini, Enrico Miglierina, Łukasz Piasecki, and Libor Veselý, Rethinking polyhedrality for Lindenstrauss spaces, Israel J. Math. 216 (2016), no. 1, 355–369. MR 3556971, DOI 10.1007/s11856-016-1412-8
- A. J. Lazar and J. Lindenstrauss, On Banach spaces whose duals are $L_{1}$ spaces, Israel J. Math. 4 (1966), 205–207. MR 206670, DOI 10.1007/BF02760079
- A. J. Lazar and J. Lindenstrauss, Banach spaces whose duals are $L_{1}$ spaces and their representing matrices, Acta Math. 126 (1971), 165–193. MR 291771, DOI 10.1007/BF02392030
- E. Michael and A. Pełczyński, Separable Banach spaces which admit $l_{n}{}^{\infty }$ approximations, Israel J. Math. 4 (1966), 189–198. MR 211247, DOI 10.1007/BF02760077
- Z. Semadeni, Free compact convex sets, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 13 (1965), 141–146 (English, with Russian summary). MR 190719
- M. Zippin, On some subspaces of Banach spaces whose duals are $L_{1}$ spaces, Proc. Amer. Math. Soc. 23 (1969), 378–385. MR 246094, DOI 10.1090/S0002-9939-1969-0246094-0
Additional Information
- M. Zippin
- Affiliation: Department of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel
- MR Author ID: 214924
- Email: zippin@math.huji.ac.il
- Received by editor(s): January 19, 2018
- Received by editor(s) in revised form: April 4, 2018
- Published electronically: September 17, 2018
- Communicated by: Thomas Schlumprecht
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 5257-5262
- MSC (2010): Primary 46B04, 46B25
- DOI: https://doi.org/10.1090/proc/14196
- MathSciNet review: 3866864