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

Source: [Asymptotical behavior of subspaces under action of asymptotically finite-dimensional semigroups of operators](<https://www.sota2.com/research/paper/68fa4cdb1e209131ce94fe80>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T09:00:22.804Z

Authors: K.Storozhuk

Published: 2004-02-09T14:18:08.000Z

## Abstract

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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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/math/0402123>)

[PDF](<https://arxiv.org/pdf/math/0402123.pdf>)