| The Representation of Continuous Linear Operator by Integral |
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| 作者姓名： | 曾韧英 |
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| 作者单位： | Department of Mathematics，Chongqing Teacher's College，Chongqing，630047 |
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| 摘 要： | LetXoverthefieldKstandforacompletelocallyconvexspace,andweassumethatitstopologyisgeneratedbyafamilyPofcontinuousseminormsonX,Let(O,Z,p)beafinitepositivemeasurespace.Afunctionf:Q-Xissaidtobep-integrable(forthedefinition,see1]),ifthereexistsasequence{ft}ofsimplefunctionssuchthat.,ThislimitexistsandisinX.Denote,p)asthespaceofcIassesofNintegrablefunctionswhereLfj=Lgjifandonlyiff=gP-a.e..Putq(f)=j.p(f)dp,foreachpeP.ThetopologyonL1(p,Z)consideredisthese,generatedbyalltheq.L.EggheLlIhaspro…
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| 关 键 词： | 连续线性算子 积分表示 FreChet空间 |
The Representation of Continuous Linear Operator by Integral |
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| Zeng Renying.The Representation of Continuous Linear Operator by Integral[J].Chinese Quarterly Journal of Mathematics,1997,12(3):41-44. |
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| Authors: | Zeng Renying |
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| Abstract: | In this paper,we study the representation of linear operator on but abandom the Radon-Nikodym property and give a necessary and sufficient condition for representability of linear operator on by integral. |
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