Spectral localization, power boundedness and invariant subspaces under Ritt's type condition
Studia Mathematica, Tome 134 (1999) no. 2, pp. 153-167
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
For a bounded linear operator T in a Banach space the Ritt resolvent condition $∥R_λ(T)∥ ≤ C/|λ - 1|$ (|λ| > 1) can be extended (changing the constant C) to any sector |arg(λ - 1)| ≤ π - δ, $arccos(C^{-1}) δ π/2$. This implies the power boundedness of the operator T. A key result is that the spectrum σ(T) is contained in a special convex closed domain. A generalized Ritt condition leads to a similar localization result and then to a theorem on invariant subspaces.
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author = {Yu Lyubich},
title = {Spectral localization, power boundedness and invariant subspaces under {Ritt's} type condition},
journal = {Studia Mathematica},
pages = {153--167},
publisher = {mathdoc},
volume = {134},
number = {2},
year = {1999},
doi = {10.4064/sm-134-2-153-167},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-134-2-153-167/}
}
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Yu Lyubich. Spectral localization, power boundedness and invariant subspaces under Ritt's type condition. Studia Mathematica, Tome 134 (1999) no. 2, pp. 153-167. doi: 10.4064/sm-134-2-153-167
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