On the strongly extreme points of convex bodies in separable Banach spaces

Authors:
B. V. Godun, Bor-Luh Lin and S. L. Troyanski

Journal:
Proc. Amer. Math. Soc. **114** (1992), 673-675

MSC:
Primary 46B20; Secondary 52A07

MathSciNet review:
1070518

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Abstract: Every separable Banach space admits an equivalent norm such that the unit ball with respect to this norm has at most countably many strongly extreme points. Every separable nonreflexive Banach space can be renormed so that its unit ball has at most countably many weakly strongly extreme points.

**[F]**V. P. Fonf,*A property of Lindenstrauss-Phelps spaces*, Funktsional. Anal. i Prilozhen.**13**(1979), no. 1, 79–80 (Russian). MR**527533****[KR]**Ken Kunen and Haskell Rosenthal,*Martingale proofs of some geometrical results in Banach space theory*, Pacific J. Math.**100**(1982), no. 1, 153–175. MR**661446****[LP]**Joram Lindenstrauss and R. R. Phelps,*Extreme point properties of convex bodies in reflexive Banach spaces.*, Israel J. Math.**6**(1968), 39–48. MR**0234260****[R1]**Haskell Rosenthal,*On non-norm-attaining functionals and the equivalence of the weak*-KMP with the RNP*, Texas Functional Analysis Seminar 1985–1986 (Austin, TX, 1985–1986), Longhorn Notes, Univ. Texas, Austin, TX, 1986, pp. 1–12. MR**1017038****[R2]**-,*On the structure of non-dentable closed bounded convex sets*, Adv. in Math.**70**(1988), 1-58.

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1992-1070518-5

Keywords:
Strongly extreme points,
weakly strongly extreme points,
weak*-extreme points,
reflexive Banach spaces,
equivalent norm

Article copyright:
© Copyright 1992
American Mathematical Society