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Asymptotical behavior of subspaces under action of asymptotically finite-dimensional semigroups of operators

K. Storozhuk
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Abstract

We study a semigroup $ϕ$ of linear operators acting on a Banach space $X$ which satisfies the condition $\codim X_0<\infty$, where $X_0=\{x\in X \mid ϕ_t(x)\underset{t\to\infty}\longrightarrow 0\}.$ We show that $X_0$ is closed under these conditions. We establish some properties concerning the asymptotic behavior of subspaces which complement $X_0$ in $X$.

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K. Storozhuk. 2004-02-09. Asymptotical behavior of subspaces under action of asymptotically finite-dimensional semigroups of operators. https://arxiv.org/abs/math/0402123

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