Multiplication in Vector Lattices
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1136-1149

Voir la notice de l'article provenant de la source Cambridge University Press

B. Z. Vulih has shown (13) how an essentially unique intrinsic multiplication can be defined in a Dedekind complete vector lattice L having a weak order unit. Since this work is available only in Russian, a brief outline is given in § 2 (cf. also the review by E. Hewitt (4), and for details, consult (13) or (11)).
Rice, Norman M. Multiplication in Vector Lattices. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1136-1149. doi: 10.4153/CJM-1968-108-0
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[1] 1. Amemiya, I., A generalization of the Riesz-Fischer theorem, J. Math. Soc. Japan 5 (1953), 353–354. Google Scholar

[2] 2. Bourbaki, N., Éléments de mathématique. XIII. Première partie: Les structures fondamentales de l'analyse. Livre VI: Intégration, Actualités Sci. Indust., no. 1175 (Hermann, Paris, 1952). Google Scholar

[3] 3. Freudenthal, H., Teilweise geordnete Moduln, Proc. Acad. Sci. Amsterdam 39 (1936), 641–651. Google Scholar

[4] 4. Hewitt, E. (Review of a paper of B. Z. Vulih), The product in linear partially ordered spaces and its applications to the theory of operators. I and II, Math. Reviews 10 (1949), 46. Google Scholar

[5] 5. Johnson, D. G. and Kist, J. E., Prime ideals in vector lattices, Can. J. Math. 14 (1962), 517–528. Google Scholar

[6] 6. Luxemburg, W. A. J. and Zaanen, A. C., Notes on Banach function spaces, Proc. Acad. Sci. Amsterdam, Note II, A66 (1963), 148-153, Note VI, ibid., 655-668; Note VII, ibid., 669-681; Note VIII, A67 (1964), 104-119; Note IX, ibid., 360–376. Google Scholar

[7] 7. Nakano, H., Modern spectral theory (Maruzen, Tokyo, 1950). Google Scholar

[8] 8. Pinsker, A. G., Sur l'extension des espaces semi-or donnés, Dokl. Akad. Nauk SSSR 21 1938), 6–9. Google Scholar

[9] 9. Pinsker, A. G., Sur certaines propriétés des K-espaces étendus, Dokl. Akad. Nauk SSSR 22 (1939), 216–219. Google Scholar

[10] 10. Pinsker, A. G., On representations of a K-space as a ring of self-adjoint operators, Dokl. Akad. Nauk SSSR 106 (1956), 195–198. (Russian) Google Scholar

[11] 11. Rice, N. M., Multiplication in Riesz spaces (Thesis, California Institute of Technology, 1966). Google Scholar

[12] 12. Segal, I. E., Equivalences of measure spaces, Amer. J. Math. 73 (1951), 275–313. Google Scholar

[13] 13. Vulih, B. Z., The product in linear partially ordered spaces and its applications to the theory of operators, Mat. Sb. (N.S.) 22 (52) (1948); I, 27-78; II, 267–317. (Russian) Google Scholar

[14] 14. Zaanen, A. C., An introduction to the theory of intgreation (North-Holland, Amsterdam, 1961). Google Scholar

[15] 15. Zaanen, A. C., The Radon-Nikodym theorem, Proc. Acad. Sci. Amsterdam, A64 (1961); I, 157-170; II, 171–187.10.1016/S1385-7258(61)50017-0 Google Scholar | DOI

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