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On ergodicity for operators with bounded resolvent in Banach spaces
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2011 (English)In: Studia Mathematica, ISSN 0039-3223, E-ISSN 1730-6337, Vol. 204, no 1, 63-72 p.Article in journal (Refereed) Published
Abstract [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 the norms of alpha(alpha - A)(-1) are uniformly bounded for all alpha > 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 assuming that the product of the norms of I - 2P and I - Q is less than 2 where Q is a projection depending on the operator A. For the space of James we show that the norm of I - 2P is less than 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 delta, the operators T(t) - I, 0 < t < delta, are also ergodic.

Place, publisher, year, edition, pages
2011. Vol. 204, no 1, 63-72 p.
Keyword [en]
ergodicity, bounded resolvent, canonical projection, semigroups of operators
National Category
URN: urn:nbn:se:kth:diva-38156DOI: 10.4064/sm204-1-4ISI: 000293110900004ScopusID: 2-s2.0-80051776581OAI: diva2:435996

QC 20150720

Available from: 2011-08-22 Created: 2011-08-22 Last updated: 2015-07-20Bibliographically approved

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Mattila, Kirsti
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