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Fundam. Prikl. Mat., 1997, Volume 3, Issue 3, Pages 937–946 (Mi fpm252)  

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

On question about invariant subspaces of locally convex spaces

O. D. Solomatin

Orel State University

Abstract: Subspaces of complete locally convex space $H$, invariant to linear continuous operator of finite order and type, are investigated. Subspaces, invariant to generalized displacement that is generated by this operator, are also researched. In particular, it is proved that in every subspace, invariant in respect to this operator, and admitting spectrum synthesis, there is a vector, generating this subspace. It is proved too, that every subspace, invariant in respect to generalization displacement, is invariant in respect to the operator, which generates this displacement and vice versa.

Full text: PDF file (400 kB)

Bibliographic databases:
UDC: 517.984
Received: 01.02.1996

Citation: O. D. Solomatin, “On question about invariant subspaces of locally convex spaces”, Fundam. Prikl. Mat., 3:3 (1997), 937–946

Citation in format AMSBIB
\Bibitem{Sol97}
\by O.~D.~Solomatin
\paper On question about invariant subspaces of locally convex spaces
\jour Fundam. Prikl. Mat.
\yr 1997
\vol 3
\issue 3
\pages 937--946
\mathnet{http://mi.mathnet.ru/fpm252}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1794151}
\zmath{https://zbmath.org/?q=an:0935.47005}


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    This publication is cited in the following articles:
    1. S. N. Mishin, “Invariance of the Order and Type of a Sequence of Operators”, Math. Notes, 100:3 (2016), 429–437  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
  • Фундаментальная и прикладная математика
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