Abstract:
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.
\Bibitem{Nai76}
\by M.~A.~Naimark
\paper The direct integral of pairs of dual spaces
\jour Math. USSR-Izv.
\yr 1976
\vol 10
\issue 2
\pages 339--349
\mathnet{http://mi.mathnet.ru/eng/im2113}
\crossref{https://doi.org/10.1070/IM1976v010n02ABEH001693}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=410318}
\zmath{https://zbmath.org/?q=an:0365.46007}
Linking options:
https://www.mathnet.ru/eng/im2113
https://doi.org/10.1070/IM1976v010n02ABEH001693
https://www.mathnet.ru/eng/im/v40/i2/p355
This publication is cited in the following 3 articles:
I. M. Gel'fand, M. I. Graev, D. P. Zhelobenko, R. S. Ismagilov, M. G. Krein, L. D. Kudryavtsev, S. M. Nikol'skii, A. Ya. Helemskii, A. V. Strauss, “Mark Aronovich Naimark (obituary)”, Russian Math. Surveys, 35:4 (1980), 157–164
Hitoshi SHIN'YA, “On a decomposability of homogeneous linear system representations of locally compact groups”, Jpn. j. math, 6:2 (1980), 229
M. A. Naimark, “A criterion for the decomposability of a homogeneous representation of a locally
compact group into a direct integral of its irreducible representations”, Math. USSR-Izv., 10:3 (1976), 515–533
Citation in format AMSBIB
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