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Sibirsk. Mat. Zh., 2003, Volume 44, Number 6, Pages 1365–1376 (Mi smj1262)  

Stabilizability in asymptotically finite-dimensional semigroups

K. V. Storozhuk

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We study a semigroup $\varphi$ of linear operators on a Banach space $X$ which satisfies the condition $\operatorname{codim}X_0<\infty$, where $X_0=\{x\in X|\varphi_t(x)\xrightarrow[t\to\infty] 0\}$. We show that $X_0$ is closed and establish some properties of the asymptotic behavior of the subspaces complementing $X_0$ to $X$.

Keywords: semigroup of linear operators, invariant subspace of a semigroup

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English version:
Siberian Mathematical Journal, 2003, 44:6, 1075–1084

Bibliographic databases:

UDC: 517.986.7
Received: 01.11.2002

Citation: K. V. Storozhuk, “Stabilizability in asymptotically finite-dimensional semigroups”, Sibirsk. Mat. Zh., 44:6 (2003), 1365–1376; Siberian Math. J., 44:6 (2003), 1075–1084

Citation in format AMSBIB
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\by K.~V.~Storozhuk
\paper Stabilizability in asymptotically finite-dimensional semigroups
\jour Sibirsk. Mat. Zh.
\yr 2003
\vol 44
\issue 6
\pages 1365--1376
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2034942}
\zmath{https://zbmath.org/?q=an:1050.47040}
\transl
\jour Siberian Math. J.
\yr 2003
\vol 44
\issue 6
\pages 1075--1084
\crossref{https://doi.org/10.1023/B:SIMJ.0000007483.94529.ba}
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