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 Fundam. Prikl. Mat.: Year: Volume: Issue: Page: Find

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

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.

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Bibliographic databases:
UDC: 517.984

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} 

• http://mi.mathnet.ru/eng/fpm252
• http://mi.mathnet.ru/eng/fpm/v3/i3/p937

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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
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