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This article is cited in 1 scientific paper (total in 2 paper)
The direct integral of pairs of dual spaces
M. A. Naimark
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.
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Mathematics of the USSR-Izvestiya, 1976, 10:2, 339–349
Bibliographic databases:
UDC:
513.88+517.397
MSC: Primary 46A20, 46G99; Secondary 46B10, 46C10 Received: 06.11.1973
Citation:
M. A. Naimark, “The direct integral of pairs of dual spaces”, Izv. Akad. Nauk SSSR Ser. Mat., 40:2 (1976), 355–365; Math. USSR-Izv., 10:2 (1976), 339–349
Citation in format AMSBIB
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\by M.~A.~Naimark
\paper The direct integral of pairs of dual spaces
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1976
\vol 40
\issue 2
\pages 355--365
\mathnet{http://mi.mathnet.ru/izv2113}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=410318}
\zmath{https://zbmath.org/?q=an:0365.46007}
\transl
\jour Math. USSR-Izv.
\yr 1976
\vol 10
\issue 2
\pages 339--349
\crossref{https://doi.org/10.1070/IM1976v010n02ABEH001693}
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http://mi.mathnet.ru/eng/izv2113 http://mi.mathnet.ru/eng/izv/v40/i2/p355
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This publication is cited in the following articles:
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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
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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
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