On ergodicity for operators with bounded resolvent in Banach spaces

• Autorzy: Kirsti Mattila
• 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.

Kategorie tematyczne

• 47D06: One-parameter semigroups and linear evolution equations
• 47A35: Ergodic theory
• 46B20: Geometry and structure of normed linear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 204
• Numer: 1
• Strony: 63-72

Daty

wydano

2011

Twórcy

autor

Kirsti Mattila

• Department of Mathematics, Royal Institute of Technology, SE-10044 Stockholm, Sweden

Identyfikatory

DOI

10.4064/sm204-1-4