A short proof of the equivalence of KMP and RNP in Banach lattices and preduals of von Neumann algebras
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- by V. Caselles
- Proc. Amer. Math. Soc. 102 (1988), 973-974
- DOI: https://doi.org/10.1090/S0002-9939-1988-0934876-0
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Abstract:
In this note we give a unified approach to the equivalence between the Krein-Milman property and the Radon-Nikodym property in Banach lattices and preduals of von Neumann algebras.References
- J. Bourgain, A geometric characterization of the Radon-Nikodým property in Banach spaces, Compositio Math. 36 (1978), no. 1, 3–6. MR 515034
- Jean Bourgain and Michel Talagrand, Dans un espace de Banach reticulé solide, la propriété de Radon-Nikodým et celle de Kreĭn-Mil′man sont équivalentes, Proc. Amer. Math. Soc. 81 (1981), no. 1, 93–96 (French). MR 589144, DOI 10.1090/S0002-9939-1981-0589144-X
- Cho-Ho Chu, A note on scattered $C^{\ast }$-algebras and the Radon-Nikodým property, J. London Math. Soc. (2) 24 (1981), no. 3, 533–536. MR 635884, DOI 10.1112/jlms/s2-24.3.533
- N. Ghoussoub and M. Talagrand, Order dentability and the Radon-Nikodým property in Banach lattices, Math. Ann. 243 (1979), no. 3, 217–225. MR 548802, DOI 10.1007/BF01424542
- Helmut H. Schaefer, Banach lattices and positive operators, Die Grundlehren der mathematischen Wissenschaften, Band 215, Springer-Verlag, New York-Heidelberg, 1974. MR 0423039
- Helmut H. Schaefer, Topological vector spaces, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1966. MR 0193469
- Masamichi Takesaki, Theory of operator algebras. I, Springer-Verlag, New York-Heidelberg, 1979. MR 548728
Bibliographic Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 102 (1988), 973-974
- MSC: Primary 46B22; Secondary 46G10, 46L10
- DOI: https://doi.org/10.1090/S0002-9939-1988-0934876-0
- MathSciNet review: 934876