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Mat. Zametki, 1968, Volume 3, Issue 3, Pages 253–260 (Mi mz6676)  

This article is cited in 1 scientific paper (total in 1 paper)

Extension of dual subspaces invariant under an algebra

E. A. Larionov

Moscow Institute of Physics and Technology

Abstract: Phillips' known hypothesis concerning the extension of dual pairs of subspaces $\{\mathfrak L_1^0,\mathfrak L_2^0\}$, invariant under a commutative $J$-symmetric algebra $R$ in a Hilbert space $\mathfrak H$ , to a dual pair of maximal subspaces $\{\mathfrak L_1,\mathfrak L_2\}$, invariant under $R$ is established in the case where a dual pair of maximal subspaces exists $\{\mathfrak F_1,\mathfrak F_2\}$, invariant under $R$ with $\overline{\mathfrak F_1\oplus\mathfrak F_2}=\mathfrak H$, and the pair $\{\mathfrak L_1^0,\mathfrak L_2^1\}$ consists of $J$-neutral subspaces.

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English version:
Mathematical Notes, 1968, 3:3, 163–166

Bibliographic databases:

UDC: 513.88
Received: 27.05.1967

Citation: E. A. Larionov, “Extension of dual subspaces invariant under an algebra”, Mat. Zametki, 3:3 (1968), 253–260; Math. Notes, 3:3 (1968), 163–166

Citation in format AMSBIB
\Bibitem{Lar68}
\by E.~A.~Larionov
\paper Extension of dual subspaces invariant under an algebra
\jour Mat. Zametki
\yr 1968
\vol 3
\issue 3
\pages 253--260
\mathnet{http://mi.mathnet.ru/mz6676}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=234266}
\zmath{https://zbmath.org/?q=an:0164.16504}
\transl
\jour Math. Notes
\yr 1968
\vol 3
\issue 3
\pages 163--166
\crossref{https://doi.org/10.1007/BF01387327}


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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. 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
  • Математические заметки Mathematical Notes
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