Geodesic
The direct integral of pairs of dual spaces
Izvestiya. Mathematics, Tome 10 (1976) no. 2, pp. 339-349 
M. A. Naimark. The direct integral of pairs of dual spaces. Izvestiya. Mathematics, Tome 10 (1976) no. 2, pp. 339-349. http://geodesic.mathdoc.fr/item/IM2_1976_10_2_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

For a family of pairs of vector spaces which are in duality, given on a measure space, we introduce the concept of the direct integral, which is also a pair of vector spaces in duality; and we investigate its properties. We prove that the von Neumann direct integral of Hilbert spaces is a particular case of the direct integral defined here. Bibliography: 9 titles.

[1] Naimark M. A., “O pryamom integrale par dvoistvennykh prostranstv”, Dokl. AN SSSR, 217:4 (1974), 762–765 | MR | Zbl

[2] Burbaki N., Topologicheskie vektornye prostranstva, IIL, M., 1959

[3] Fell J. M. G., “Non-unitary dual spaces of groups”, Acta Math., 114 (1965), 267–310 | DOI | MR | Zbl

[4] Burbaki N., Obschaya topologiya; osnovnye struktury, Fizmatgiz, M., 1958

[5] Burbaki N., Integrirovanie (mery, integrirovanie mer), Nauka, M., 1967 | MR

[6] Edvards R., Funktsionalnyi analiz, Mir, M., 1969

[7] Neumann J. V., “On rings of operators. Reduction theory”, Ann. Math., 50 (1949), 401–485 | DOI | MR | Zbl

[8] Dixmier J., Les algèhres d'operateurs dans l'espace hilbertien (Algèbres de von Neumann, Paris, 1957

[9] Naimark M. A., Normirovannye koltsa, Nauka, M., 1968 | MR | Zbl