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

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

2004-02-09

arxiv.org/abs/math/0402123v1

Mathematics

Functional Analysis

10 pages

Scientific paper

We study a semigroup $\phi$ of linear operators acting on a Banach space $X$
which satisfies the condition $\codim X_0<\infty$, where $X_0=\{x\in X \mid
\phi_t(x)\underset{t\to\infty}\longrightarrow 0\}.$ 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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