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On ergodicity for operators with bounded resolvent in Banach spaces

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Mattila K.

Studia Mathematica

2011

tom 204

nr 1

63-72

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.

Ograniczanie wyników

1 Studia Mathematica

1 Mattila K.

1 2011

Wyniki wyszukiwania

On ergodicity for operators with bounded resolvent in Banach spaces