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## Studia Mathematica

2011 | 204 | 1 | 63-72
Tytuł artykułu

### On ergodicity for operators with bounded resolvent in Banach spaces

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Języki publikacji
EN
Abstrakty
EN
We prove results on ergodicity, i.e. on the property that the space is a direct sum of the kernel of an operator and the closure of its range, for closed linear operators A such that $||α(α - A)^{-1}||$ is uniformly bounded for all α > 0. We consider operators on Banach spaces which have the property that the space is complemented in its second dual space by a projection P. Results on ergodicity are obtained under a norm condition ||I - 2P|| ||I - Q|| < 2 where Q is a projection depending on the operator A. For the space of James we show that ||I - 2P|| < 2 where P is the canonical projection of the predual of the space. If $(T(t))_{t≥0}$ is a bounded strongly continuous and eventually norm continuous semigroup on a Banach space, we show that if the generator of the semigroup is ergodic, then, for some positive number δ, the operators T(t) - I, 0 < t < δ, are also ergodic.
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Rocznik
Tom
Numer
Strony
63-72
Opis fizyczny
Daty
wydano
2011
Twórcy
autor
• Department of Mathematics, Royal Institute of Technology, SE-10044 Stockholm, Sweden
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