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

2004/02/09 by K. V. Storozhuk, K. Storozhuk, Storozhuk, K.
Mathematics · #Differential Equations and Boundary Problems #Spectral Theory in Mathematical Physics #advanced mathematical theories #math.FA #msc:47D03

paper · pdf · doi:10.48550/arxiv.math/0402123

10 pages

arxiv created 2004/02/09 · arxiv updated 2009/12/01

Abstract

We study a semigroup ϕ of linear operators acting on a Banach space X which satisfies the condition \codim X₀<∞, where X₀=\x∈ X | ϕ_t(x)\undersett→∞\longrightarrow 0\. We show that X₀ is closed under these conditions. We establish some properties concerning the asymptotic behavior of subspaces which complement X₀ in X.

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