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1IntroductionLetXbea'Banachspace,andB(X)betheBanachspaceofcontinuouslinearoperatorsfromXintoX.LetT(t)bea(CO)selltigroup,andletAbeitsinfinitesilllalgenerator.WedenotethedomainandtherangeofAbyD(A)andR(A).LetBbelongtoB(X).FOrthelinearsystem:andthedelaylinearsystem:wherer>0,((.)EC([--.,o],x)={fif:[--r,oj~X,fiscontinuous},r(t)EC[o,.)'05r(t)5r.Weconsidertileexponentialstabilityequivalencebetweellthesolutionof(1)and(2),whichllleans:ifthereexistM,a>0,sllththatIIS(f)II5Me--"'(f20),whereS(… 相似文献
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A Generalization of C—semigroup 总被引:3,自引:0,他引:3
§ 1.TheGeneralC semigroup Inthispaper,weletXbeaBanachspace,andB(X)thespaceofallboundedlinearoperatorsfromXintoX . Definition 1 .1 SupposeCisaboundedinjectiveoperatorfromXintoX .Thefamilyofboundedlinearoperators (S(t) ) t≥ 0 isageneralC semigroupifithasthefollowing… 相似文献
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令M为可分的Ⅱ_(1)型von Neumann代数.我们证明了,如果M具有性质Γ,G为可数顺从群且α是G在M上保迹的真外作用,则交叉积M■αG为具有性质Γ的Ⅱ_(1)型von Neumann代数. 相似文献
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