Spectral localization, power boundedness and invariant subspaces under Ritt's type condition
Lyubich, Yu.
Studia Mathematica, Tome 133 (1999), p. 153-167 / Harvested from The Polish Digital Mathematics Library
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For a bounded linear operator T in a Banach space the Ritt resolvent condition ∥Rλ(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.

Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:216629 
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Lyubich, Yu. Spectral localization, power boundedness and invariant subspaces under Ritt's type condition. Studia Mathematica, Tome 133 (1999) pp. 153-167. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv134i2p153bwm/

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