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Uspekhi Mat. Nauk, 1962, Volume 17, Issue 4(106), Pages 3–56 (Mi umn6512)  

This article is cited in 23 scientific papers (total in 23 papers)

The geometry of infinite-dimensional spaces with a bilinear metric

Yu. P. Ginzburg, I. S. Iokhvidov


Full text: PDF file (6280 kB)

English version:
Russian Mathematical Surveys, 1962, 17:4, 1–51

Bibliographic databases:

MSC: 47A07, 15A63, 46E50, 47A15, 54B05
Received: 08.01.1962

Citation: Yu. P. Ginzburg, I. S. Iokhvidov, “The geometry of infinite-dimensional spaces with a bilinear metric”, Uspekhi Mat. Nauk, 17:4(106) (1962), 3–56; Russian Math. Surveys, 17:4 (1962), 1–51

Citation in format AMSBIB
\Bibitem{GinIok62}
\by Yu.~P.~Ginzburg, I.~S.~Iokhvidov
\paper The geometry of infinite-dimensional spaces with a~bilinear metric
\jour Uspekhi Mat. Nauk
\yr 1962
\vol 17
\issue 4(106)
\pages 3--56
\mathnet{http://mi.mathnet.ru/umn6512}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=145319}
\zmath{https://zbmath.org/?q=an:0144.37303|0111.30601}
\transl
\jour Russian Math. Surveys
\yr 1962
\vol 17
\issue 4
\pages 1--51
\crossref{https://doi.org/10.1070/RM1962v017n04ABEH004117}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Gerd Wittstock, “Über invariante Teilräume zu positiven Transformationen in Räumen mit indefiniter Metrik”, Math Ann, 172:3 (1967), 167  crossref  mathscinet
    2. R. S. Ismagilov, “Elementary spherical functions on the group $SL(2,P)$ over a field $P$, which is not locally compact, with respect to the subgroup of matrices with integral elements”, Math. USSR-Izv., 1:2 (1967), 349–380  mathnet  crossref  mathscinet  zmath
    3. E. A. Larionov, “On the number of fixed points of a linear-fractional transformation of an operator ball onto itself”, Math. USSR-Sb., 7:2 (1969), 195–204  mathnet  crossref  mathscinet  zmath
    4. E. A. Larionov, “Self-adjoint quadratic bundles”, Math. USSR-Izv., 3:1 (1969), 131–145  mathnet  crossref  mathscinet  zmath
    5. J.William Helton, “Unitary operators on a space with an indefinite inner product”, Journal of Functional Analysis, 6:3 (1970), 412  crossref
    6. Yu. L. Shmul'yan, “Extended resolvents and extended spectral functions of a Hermitian operator”, Math. USSR-Sb., 13:3 (1971), 435–450  mathnet  crossref  mathscinet  zmath
    7. T. Ya. Azizov, I. S. Iokhvidov, “Linear operators in Hilbert spaces with $G$-metric”, Russian Math. Surveys, 26:4 (1971), 45–97  mathnet  crossref  mathscinet  zmath
    8. T. Ya. Azizov, “Dissipative operators in a Hilbert space with an indefinite metric”, Math. USSR-Izv., 7:3 (1973), 639–660  mathnet  crossref  mathscinet  zmath
    9. O. I. Zavialov, “Wick polynomials in a space with indefinite metric”, Theoret. and Math. Phys., 16:2 (1973), 735–742  mathnet  crossref  mathscinet  zmath
    10. Yu. L. Shmul'yan, “Extension theory for operators and spaces with indefinite metric”, Math. USSR-Izv., 8:4 (1974), 895–907  mathnet  crossref  mathscinet  zmath
    11. Yu. L. Shmul'yan, “On closed Hermitian operators and their selfadjoint extensions”, Math. USSR-Sb., 22:2 (1974), 151–166  mathnet  crossref  mathscinet  zmath
    12. V. A. Khatskevich, “On fixed points of generalized linear-fractional transformations”, Math. USSR-Izv., 9:5 (1975), 1069–1079  mathnet  crossref  mathscinet  zmath
    13. R. A. Krajcik, “Bhabha first-order wave equations. V. Indefinite metric and Foldy-Wouthuysen transformations”, Phys Rev D, 14:2 (1976), 418  crossref  mathscinet  adsnasa
    14. Yu. L. Shmul'yan, “The theory of linear relations and spaces with an indefinite metric”, Funct. Anal. Appl., 10:1 (1976), 56–60  mathnet  crossref  mathscinet  zmath
    15. V. A. Khatskevich, “An application of the contraction mapping principle in the theory of operators in an indefinite metric space”, Funct. Anal. Appl., 12:1 (1978), 70–71  mathnet  crossref  mathscinet  zmath
    16. Schôichi Ôta, “Certain operator algebras induced by ∗-derivations in C∗-algebras on an indefinite inner product space”, Journal of Functional Analysis, 30:2 (1978), 238  crossref
    17. M. M. Mel'tser, “Classification of von Neumann $J$-algebras”, Funct. Anal. Appl., 13:4 (1979), 305–307  mathnet  crossref  mathscinet  zmath
    18. Yu. L. Shmul'yan, “Transformers of linear relations in $J$-spaces”, Funct. Anal. Appl., 14:2 (1980), 110–113  mathnet  crossref  mathscinet  zmath
    19. K. Yu. Dadashyan, S. S. Horuzhy, “On field algebras in quantum theory with indefinite metric”, Theoret. and Math. Phys., 54:1 (1983), 35–48  mathnet  crossref  mathscinet  zmath  isi
    20. Daniel Alpay, Harry Dym, “Structured invariant spaces of vector valued functions, sesquilinear forms, and a generalization of the lohvidov laws”, Linear Algebra and its Applications, 137-138 (1990), 413  crossref
    21. Seppo Hassi, Kenneth Nordström, “On projections in a space with an indefinite metric”, Linear Algebra and its Applications, 208-209 (1994), 401  crossref
    22. P. G. Grinevich, S. P. Novikov, “Singular finite-gap operators and indefinite metrics”, Russian Math. Surveys, 64:4 (2009), 625–650  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    23. D. S. Bykov, Yu. F. Dolgii, “Kanonicheskie approksimatsii v zadache optimalnoi stabilizatsii avtonomnykh sistem s posledeistviem”, Tr. IMM UrO RAN, 17, no. 2, 2011, 20–34  mathnet  elib
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