no. 1
The Poulsen simplex
Annales de l'Institut Fourier, Volume 28 (1978) no. 1, pp. 91-114.

It is proved that there is a unique metrizable simplex S whose extreme points are dense. This simplex is homogeneous in the sense that for every 2 affinely homeomorphic faces F 1 and F 2 there is an automorphism of S which maps F 1 onto F 2 . Every metrizable simplex is affinely homeomorphic to a face of S. The set of extreme points of S is homeomorphic to the Hilbert space ℓ 2 . The matrices which represent A(S) are characterized.

On démontre ici qu’il existe un seul simplexe métrisable S dont les points extrémaux sont denses. Ce simplexe est homogène au sens que pour tout couple de face F 1 , F 2 affinement homéomorphes, il existe un automorphisme de S qui transforme F 1 en F 2 . Tout simplexe métrisable est affinement homéomorphe à une face de S. L’ensemble des points extrémaux de S est homéomorphe à l’espace de Hilbert ℓ 2 . On caractérise les matrices qui représentent A(S).

@article{AIF_1978__28_1_91_0,
     author = {Lindenstrauss, Joram and Olsen, Gunnar and Sternfeld, Y.},
     title = {The {Poulsen} simplex},
     journal = {Annales de l'Institut Fourier},
     pages = {91--114},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {28},
     number = {1},
     year = {1978},
     doi = {10.5802/aif.682},
     zbl = {0363.46006},
     mrnumber = {80b:46019a},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.682/}
}
TY  - JOUR
AU  - Lindenstrauss, Joram
AU  - Olsen, Gunnar
AU  - Sternfeld, Y.
TI  - The Poulsen simplex
JO  - Annales de l'Institut Fourier
PY  - 1978
SP  - 91
EP  - 114
VL  - 28
IS  - 1
PB  - Institut Fourier
PP  - Grenoble
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.682/
DO  - 10.5802/aif.682
LA  - en
ID  - AIF_1978__28_1_91_0
ER  - 
%0 Journal Article
%A Lindenstrauss, Joram
%A Olsen, Gunnar
%A Sternfeld, Y.
%T The Poulsen simplex
%J Annales de l'Institut Fourier
%D 1978
%P 91-114
%V 28
%N 1
%I Institut Fourier
%C Grenoble
%U https://aif.centre-mersenne.org/articles/10.5802/aif.682/
%R 10.5802/aif.682
%G en
%F AIF_1978__28_1_91_0
Lindenstrauss, Joram; Olsen, Gunnar; Sternfeld, Y. The Poulsen simplex. Annales de l'Institut Fourier, Volume 28 (1978) no. 1, pp. 91-114. doi : 10.5802/aif.682. https://aif.centre-mersenne.org/articles/10.5802/aif.682/

[1] E.M. Alfsen, Compact convex sets and boundary integrals, Springer-Verlag, 1971. | MR | Zbl

[2] C. Bessaga and A. Pelczynski, Selected topics from infinite dimensional topology, Warsaw, 1975. | Zbl

[3] A. B. Hansen and Y. Sternfeld, On the characterization of the dimension of a compact metric space K by the representing matrices of C(K), Israel. J. of Math., 22 (1975), 148-167. | MR | Zbl

[4] R. Haydon, A new proof that every polish space is the extreme boundary of a simplex, Bull. London Math, Soc., 7 (1975), 97-100. | MR | Zbl

[5] A. Lazar, Spaces of affine continuous functions on simplexes, A.M.S. Trans., 134 (1968), 503-525. | MR | Zbl

[6] A. Lazar, Affine product of simplexes, Math. Scand., 22 (1968), 165-175. | MR | Zbl

[7] A. Lazar and J. Lindenstrauss, Banach spaces whose duals are L1 spaces and their representing matrices. Acta Math., 120 (1971), 165-193. | MR | Zbl

[8] W. Lusky, The Gurari space is unique, Arch. Math., 27 (1976), 627-635. | MR | Zbl

[9] W. Lusky, On separable Lindenstrauss spaces, J. Funct. Anal., 26 (1977), 103-120. | MR | Zbl

[10] E.T. Poulsen, A simplex with dense extreme points, Ann. Inst. Fourier, Grenoble, 11 (1961), 83-87. | Numdam | MR | Zbl

[11] Y. Sternfeld, Characterization of Bauer simplices and some other classes of Choquet simplices by their representing matrices, to appear.

[12] P. Wojtaszczyk, Some remarks on the Gurari space, Studia Math., XLI (1972), 207-210. | MR | Zbl

Cited by Sources: