# The Poulsen simplex

Joram Lindenstrauss; Gunnar Olsen; Y. Sternfeld

Annales de l'institut Fourier (1978)

- Volume: 28, Issue: 1, page 91-114
- ISSN: 0373-0956

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topLindenstrauss, Joram, Olsen, Gunnar, and Sternfeld, Y.. "The Poulsen simplex." Annales de l'institut Fourier 28.1 (1978): 91-114. <http://eudml.org/doc/74350>.

@article{Lindenstrauss1978,

abstract = {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 $\ell _2$. The matrices which represent $A(S)$ are characterized.},

author = {Lindenstrauss, Joram, Olsen, Gunnar, Sternfeld, Y.},

journal = {Annales de l'institut Fourier},

language = {eng},

number = {1},

pages = {91-114},

publisher = {Association des Annales de l'Institut Fourier},

title = {The Poulsen simplex},

url = {http://eudml.org/doc/74350},

volume = {28},

year = {1978},

}

TY - JOUR

AU - Lindenstrauss, Joram

AU - Olsen, Gunnar

AU - Sternfeld, Y.

TI - The Poulsen simplex

JO - Annales de l'institut Fourier

PY - 1978

PB - Association des Annales de l'Institut Fourier

VL - 28

IS - 1

SP - 91

EP - 114

AB - 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 $\ell _2$. The matrices which represent $A(S)$ are characterized.

LA - eng

UR - http://eudml.org/doc/74350

ER -

## References

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- [8] W. LUSKY, The Gurari space is unique, Arch. Math., 27 (1976), 627-635. Zbl0338.46023MR55 #6177
- [9] W. LUSKY, On separable Lindenstrauss spaces, J. Funct. Anal., 26 (1977), 103-120. Zbl0358.46016MR58 #12303
- [10] E.T. POULSEN, A simplex with dense extreme points, Ann. Inst. Fourier, Grenoble, 11 (1961), 83-87. Zbl0104.08402MR23 #A1224
- [11] Y. STERNFELD, Characterization of Bauer simplices and some other classes of Choquet simplices by their representing matrices, to appear. Zbl0556.46006
- [12] P. WOJTASZCZYK, Some remarks on the Gurari space, Studia Math., XLI (1972), 207-210. Zbl0233.46024MR46 #7860

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