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Transactions of the American Mathematical Society

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A characterization of $ M$-spaces in the class of separable simplex spaces


Author: Alan Gleit
Journal: Trans. Amer. Math. Soc. 169 (1972), 25-33
MSC: Primary 46A40
DOI: https://doi.org/10.1090/S0002-9947-1972-0306864-1
MathSciNet review: 0306864
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Abstract: We show that a separable simplex space is an $ M$-space iff the arbitrary intersection of closed ideals is always an ideal.


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  • [1] N. Bourbaki, Livre V: Intégration. Chap. V: Intégration des mesures, 2 ième éd., Actualités Sci. Indust., no. 1244, Hermann, Paris, 1967. MR 35 #322.
  • [2] J. Bunce, The intersection of closed ideals in a simplex space need not be an ideal, J. London Math. Soc. (2) 1 (1969), 67-68. MR 39 #6050. MR 0244736 (39:6050)
  • [3] N. Dunford and J. T. Schwartz, Linear operators. I: General theory, Pure and Appl. Math., vol. 7, Interscience, New York, 1958. MR 22 #8302. MR 0117523 (22:8302)
  • [4] D. A. Edwards, Séparation des fonctions réelles définies sur un simplexe de Choquet, C. R. Acad. Sci. Paris 261 (1965), 2798-2800. MR 32 #8131. MR 0190720 (32:8131)
  • [5] E. Effros, Structure in simplexes, Acta Math. 117 (1967), 103-121. MR 34 #3287. MR 0203435 (34:3287)
  • [6] E. G. Effros and A. Gleit, Structure in simplexes. III. Composition series, Trans. Amer. Math. Soc. 142 (1969), 355-379. MR 40 #687. MR 0247421 (40:687)
  • [7] A. Gleit, On the existence of simplex spaces, Israel J. Math. 9 (1971), 199-209. MR 0279571 (43:5293)
  • [8] P. A. Meyer, Probability and potentials, English ed., Blaisdell, Waltham, Mass., 1966. MR 34 #5119. MR 0205288 (34:5119)
  • [9] R. Phelps, Lectures on Choquet's theorem, Van Nostrand, Princeton, N. J., 1966. MR 33 #1690. MR 0193470 (33:1690)
  • [10] M. Rogalski, Espaces de Banach ordonnés, simplexes, frontières de Silov et problème de Dirichlet, C. R. Acad. Sci. Paris Sér. A-B 263 (1966), A726-A729. MR 34 #4884. MR 0205048 (34:4883)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1972-0306864-1
Keywords: $ M$-space, simplex space, order ideals
Article copyright: © Copyright 1972 American Mathematical Society

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