Abstract
We study a semigroup ϕ of linear operators on a Banach space X which satisfies the condition codim X 0<∞, where \(X_0 = \{ x \in X|\varphi _t (x)\mathop \to \limits_{t \to \infty } 0\} .\) We show that X 0 is closed and establish some properties of the asymptotic behavior of the subspaces complementing X 0 to X.
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Storozhuk, K.V. Stabilizability in Asymptotically Finite-Dimensional Semigroups. Siberian Mathematical Journal 44, 1075–1084 (2003). https://doi.org/10.1023/B:SIMJ.0000007483.94529.ba
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DOI: https://doi.org/10.1023/B:SIMJ.0000007483.94529.ba