The Poulsen simplex

Lindenstrauss, Joram; Olsen, Gunnar; Sternfeld, Y.

doi:10.5802/aif.682

The Poulsen simplex

Lindenstrauss, Joram ; Olsen, Gunnar ; Sternfeld, Y.

Annales de l'Institut Fourier, Tome 28 (1978) no. 1, pp. 91-114.

Résumé
Abstract

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 $A (S)$ .

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.

EuDML MR Zbl | 3 citations dans Numdam

DOI : 10.5802/aif.682

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     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},
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     zbl = {0363.46006},
     language = {en},
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}

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Lindenstrauss, Joram; Olsen, Gunnar; Sternfeld, Y. The Poulsen simplex. Annales de l'Institut Fourier, Tome 28 (1978) no. 1, pp. 91-114. doi : 10.5802/aif.682. http://www.numdam.org/articles/10.5802/aif.682/

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