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Sibirsk. Mat. Zh., 2011, Volume 52, Number 6, Pages 1389–1393 (Mi smj2282)  

This article is cited in 3 scientific papers (total in 3 papers)

A condition for asymptotic finite-dimensionality of an operator semigroup

K. V. Storozhukab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University, Novosibirsk

Abstract: Let $X$ be a Banach space and let $T\colon X\to X$ be a power bounded linear operator. Put $X_0=\{x\in X\mid T^nx\to0\}$. Assume given a compact set $K\subset X$ such that $\liminf_{n\to\infty}\rho\{T^nx,K\}\le\eta<1$ for every $x\in X$, $\|x\|\le1$. If $\eta<\frac12$, then $\operatorname{codim}X_0<\infty$. This is true in $X$ reflexive for $\eta\in[\frac12,1)$, but fails in the general case.

Keywords: asymptotically finite-dimensional operator semigroup.

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English version:
Siberian Mathematical Journal, 2011, 52:6, 1104–1107

Bibliographic databases:

UDC: 517.983.23
Received: 15.11.2010

Citation: K. V. Storozhuk, “A condition for asymptotic finite-dimensionality of an operator semigroup”, Sibirsk. Mat. Zh., 52:6 (2011), 1389–1393; Siberian Math. J., 52:6 (2011), 1104–1107

Citation in format AMSBIB
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\pages 1389--1393
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\jour Siberian Math. J.
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\pages 1104--1107
\crossref{https://doi.org/10.1134/S0037446611060152}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. K. V. Storozhuk, “Isometries with Dense Windings of the Torus in $C(M)$”, Funct. Anal. Appl., 46:3 (2012), 232–233  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. A. G. Baskakov, I. I. Strukova, I. A. Trishina, “Solutions almost periodic at infinity to differential equations with unbounded operator coefficients”, Siberian Math. J., 59:2 (2018), 231–242  mathnet  crossref  crossref  isi  elib
    3. A. G. Baskakov, V. E. Strukov, I. I. Strukova, “Harmonic analysis of functions in homogeneous spaces and harmonic distributions that are periodic or almost periodic at infinity”, Sb. Math., 210:10 (2019), 1380–1427  mathnet  crossref  crossref  adsnasa  isi
  • Сибирский математический журнал Siberian Mathematical Journal
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