References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt152",{id:"formSmash:upper:j_idt152",widgetVar:"widget_formSmash_upper_j_idt152",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt153_j_idt156",{id:"formSmash:upper:j_idt153:j_idt156",widgetVar:"widget_formSmash_upper_j_idt153_j_idt156",target:"formSmash:upper:j_idt153:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

On ergodicity for operators with bounded resolvent in Banach spacesPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 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]

##### 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: 000293110900004ScopusID: 2-s2.0-80051776581OAI: oai:DiVA.org:kth-38156DiVA: diva2:435996
#####

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##### Note

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.

QC 20150720

Available from: 2011-08-22 Created: 2011-08-22 Last updated: 2015-07-20Bibliographically approvedReferences$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_lower_j_idt1196",{id:"formSmash:lower:j_idt1196",widgetVar:"widget_formSmash_lower_j_idt1196",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:lower:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_lower_j_idt1197_j_idt1199",{id:"formSmash:lower:j_idt1197:j_idt1199",widgetVar:"widget_formSmash_lower_j_idt1197_j_idt1199",target:"formSmash:lower:j_idt1197:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});