A note on the paper “The Poulsen Simplex” of Lindenstrauss, Olsen and Sternfeld
Annales de l'Institut Fourier, Volume 28 (1978) no. 2, pp. 233-243.

It is proved that for any f,gA(S), where S is the Poulsen simplex, so that f,g and 1-f, 1-g are smooth points, there is a rotation of A(S) carrying f in g.

On montre que pour tout f,gA(S), où S est le simplexe de Poulsen, et où f,g and 1-f, 1-g sont des points “smooth” de A(S), il existe une rotation de A(S) qui transforme f en g.

@article{AIF_1978__28_2_233_0,
     author = {Lusky, Wolfgang},
     title = {A note on the paper {{\textquotedblleft}The} {Poulsen} {Simplex{\textquotedblright}} of {Lindenstrauss,} {Olsen} and {Sternfeld}},
     journal = {Annales de l'Institut Fourier},
     pages = {233--243},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {28},
     number = {2},
     year = {1978},
     doi = {10.5802/aif.698},
     zbl = {0335.46034},
     mrnumber = {80b:46019b},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.698/}
}
TY  - JOUR
TI  - A note on the paper “The Poulsen Simplex” of Lindenstrauss, Olsen and Sternfeld
JO  - Annales de l'Institut Fourier
PY  - 1978
DA  - 1978///
SP  - 233
EP  - 243
VL  - 28
IS  - 2
PB  - Imprimerie Durand
PP  - 28 - Luisant
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.698/
UR  - https://zbmath.org/?q=an%3A0335.46034
UR  - https://www.ams.org/mathscinet-getitem?mr=80b:46019b
UR  - https://doi.org/10.5802/aif.698
DO  - 10.5802/aif.698
LA  - en
ID  - AIF_1978__28_2_233_0
ER  - 
%0 Journal Article
%T A note on the paper “The Poulsen Simplex” of Lindenstrauss, Olsen and Sternfeld
%J Annales de l'Institut Fourier
%D 1978
%P 233-243
%V 28
%N 2
%I Imprimerie Durand
%C 28 - Luisant
%U https://doi.org/10.5802/aif.698
%R 10.5802/aif.698
%G en
%F AIF_1978__28_2_233_0
Lusky, Wolfgang. A note on the paper “The Poulsen Simplex” of Lindenstrauss, Olsen and Sternfeld. Annales de l'Institut Fourier, Volume 28 (1978) no. 2, pp. 233-243. doi : 10.5802/aif.698. https://aif.centre-mersenne.org/articles/10.5802/aif.698/

[1] E. M. Alfsen, Compact, convex sets and boundary integrals, Berlin-Heidelberg-New York, Springer 1971. | Zbl: 0209.42601

[2] B. Fuchssteiner, Sandwich theorems and lattice semigroups, J. Functional Analysis, 16 (1974), 1-14. | MR: 49 #10619 | Zbl: 0283.06007

[3] A. J. Lazar and J. Lindenstrauss, Banach spaces whose duals are L1-spaces and their representing matrices, Acta Math., 126 (1971), 165-194. | MR: 45 #862 | Zbl: 0209.43201

[4] J. Lindenstrauss, Extension of compact operators, Men. Amer. Math. Soc., 48 (1964). | MR: 31 #3828 | Zbl: 0141.12001

[5] J. Lindenstrauss, G. Olsen and Y. Sternfeld, The Poulsen simplex, to appear in Anal. Inst. Fourier. | EuDML: 74350 | Numdam | MR: 500918 | Zbl: 0363.46006

[6] W. Lusky, On separable Lindenstrauss spaces, J. Functional Analysis, 26 (1977), 103-120. | MR: 58 #12303 | Zbl: 0358.46016

[7] W. Lusky, The Gurarij spaces are unique, Arch. Math., 27 (1976), 627-635. | MR: 55 #6177 | Zbl: 0338.46023

[8] E. T. Poulsen, A simplex with dense extreme points, Ann. Inst. Fourier (Grenoble), 11 (1961), 83-87. | EuDML: 73782 | Numdam | MR: 23 #A1224 | Zbl: 0104.08402

[9] P. Wojtaszczyk, Some remarks on the Gurarij space, Studia Math., 41 (1972), 207-210. | EuDML: 217607 | MR: 46 #7860 | Zbl: 0233.46024

Cited by Sources: