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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.

UDC: 517.984

Received: 01.02.1996

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