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Izv. Akad. Nauk SSSR Ser. Mat., 1976, Volume 40, Issue 2, Pages 355–365 (Mi izv2113)  

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.
Bibliography: 9 titles.

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English version:
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
\Bibitem{Nai76}
\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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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  mathnet  crossref  mathscinet  zmath
    2. 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  mathnet  crossref  mathscinet  zmath  adsnasa  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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