A note on the paper “The Poulsen Simplex” of Lindenstrauss, Olsen and Sternfeld

Wolfgang Lusky

Annales de l'institut Fourier (1978)

  • Volume: 28, Issue: 2, page 233-243
  • ISSN: 0373-0956

Abstract

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It is proved that for any f , g ∈ A ( 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 .

How to cite

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Lusky, Wolfgang. "A note on the paper “The Poulsen Simplex” of Lindenstrauss, Olsen and Sternfeld." Annales de l'institut Fourier 28.2 (1978): 233-243. <http://eudml.org/doc/74359>.

@article{Lusky1978,
abstract = {It is proved that for any $f,g \in A(S)$, 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 $g$.},
author = {Lusky, Wolfgang},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {2},
pages = {233-243},
publisher = {Association des Annales de l'Institut Fourier},
title = {A note on the paper “The Poulsen Simplex” of Lindenstrauss, Olsen and Sternfeld},
url = {http://eudml.org/doc/74359},
volume = {28},
year = {1978},
}

TY - JOUR
AU - Lusky, Wolfgang
TI - A note on the paper “The Poulsen Simplex” of Lindenstrauss, Olsen and Sternfeld
JO - Annales de l'institut Fourier
PY - 1978
PB - Association des Annales de l'Institut Fourier
VL - 28
IS - 2
SP - 233
EP - 243
AB - It is proved that for any $f,g \in A(S)$, 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 $g$.
LA - eng
UR - http://eudml.org/doc/74359
ER -

References

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  1. [1] E. M. ALFSEN, Compact, convex sets and boundary integrals, Berlin-Heidelberg-New York, Springer 1971. Zbl0209.42601
  2. [2] B. FUCHSSTEINER, Sandwich theorems and lattice semigroups, J. Functional Analysis, 16 (1974), 1-14. Zbl0283.06007MR49 #10619
  3. [3] A. J. LAZAR and J. LINDENSTRAUSS, Banach spaces whose duals are L1-spaces and their representing matrices, Acta Math., 126 (1971), 165-194. Zbl0209.43201MR45 #862
  4. [4] J. LINDENSTRAUSS, Extension of compact operators, Men. Amer. Math. Soc., 48 (1964). Zbl0141.12001MR31 #3828
  5. [5] J. LINDENSTRAUSS, G. OLSEN and Y. STERNFELD, The Poulsen simplex, to appear in Anal. Inst. Fourier. Zbl0363.46006
  6. [6] W. LUSKY, On separable Lindenstrauss spaces, J. Functional Analysis, 26 (1977), 103-120. Zbl0358.46016MR58 #12303
  7. [7] W. LUSKY, The Gurarij spaces are unique, Arch. Math., 27 (1976), 627-635. Zbl0338.46023MR55 #6177
  8. [8] E. T. POULSEN, A simplex with dense extreme points, Ann. Inst. Fourier (Grenoble), 11 (1961), 83-87. Zbl0104.08402MR23 #A1224
  9. [9] P. WOJTASZCZYK, Some remarks on the Gurarij space, Studia Math., 41 (1972), 207-210. Zbl0233.46024MR46 #7860

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