On the Radon-Nikodým property in Banach lattices
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- by Elias Saab PDF
- Proc. Amer. Math. Soc. 94 (1985), 736-737 Request permission
Abstract:
In his recent Memoirs, Talagrand showed that under Axiom ${\text {L}}$, the weak*-Radon-Nikodým property is equivalent to the Radon-Nikodým property in a Banach lattice. In this note we prove this result by a simple method without assuming Axiom ${\text {L}}$.References
- Nassif Ghoussoub and Elias Saab, On the weak Radon-Nikodým property, Proc. Amer. Math. Soc. 81 (1981), no. 1, 81–84. MR 589141, DOI 10.1090/S0002-9939-1981-0589141-4
- Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. II, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], vol. 97, Springer-Verlag, Berlin-New York, 1979. Function spaces. MR 540367, DOI 10.1007/978-3-662-35347-9
- Michel Talagrand, Pettis integral and measure theory, Mem. Amer. Math. Soc. 51 (1984), no. 307, ix+224. MR 756174, DOI 10.1090/memo/0307
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 94 (1985), 736-737
- MSC: Primary 46B22; Secondary 46B30, 46G10
- DOI: https://doi.org/10.1090/S0002-9939-1985-0792294-X
- MathSciNet review: 792294