Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
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
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-38156DOI: 10.4064/sm204-1-4ISI: 000293110900004Scopus ID: 2-s2.0-80051776581OAI: oai:DiVA.org:kth-38156DiVA: diva2:435996
Note

QC 20150720

Available from: 2011-08-22 Created: 2011-08-22 Last updated: 2017-12-08Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Search in DiVA

By author/editor
Mattila, Kirsti
By organisation
Mathematics (Div.)
In the same journal
Studia Mathematica
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 42 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf