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Charakterisierungen schwacher Kompaktheit in Dualräumen

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https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2003091515
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DC ElementWertSprache
dc.contributor.advisorProf. Dr. Peter Meyer-Nieberg
dc.creatorMöller, Christian
dc.date.accessioned2010-01-30T14:50:30Z
dc.date.available2010-01-30T14:50:30Z
dc.date.issued2003-09-15T19:56:27Z
dc.date.submitted2003-09-15T19:56:27Z
dc.identifier.urihttps://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2003091515-
dc.description.abstractIn this thesis we present an extensive characterization of weak* sequentially precompact subsets of the dual of a sequentially order complete M-space with an order unit. This central part of the thesis generalizes results due to H.H. Schaefer and X.D. Zhang showing that small weak* compact subsets of the dual of a space of bounded measurable real-valued functions (continuous real-valued functions on a compact quasi-Stonian space) are weakly compact. Moreover, while the proofs of Schaefer and Zhang use measure theoretical arguments, the arguments presented here are purely elementary and are based on the well-known result, that the space l1 has the Schur property. Finally some applications are given. For example, we investigate compact or sequentially precompact subsets, which consist of order-weakly compact operators, in the space of continuous linear operators defined on a sequentially order complete Riesz space with values in a Banach space provided with the strong operator topology: as an immediate consequence of the results, we can easily deduce extended versions of the Vitali-Hahn-Saks theorem for vector measures. For this we need a generalization of the Yosida-Hewitt decomposition theorem, which is proved here with other techniques like the factorization of an order-weakly compact operator through a Banach lattice with order continuous norm.ger
dc.language.isoger
dc.subjectweak compactness
dc.subjectM-space with an order unit
dc.subjectdual space
dc.subjectSchur property
dc.subjectRosenthal´s Lemma
dc.subject(order-)weakly compact operator
dc.subjectVitali-Hahn-Saks theorem
dc.subject.ddc510 - Mathematikger
dc.titleCharakterisierungen schwacher Kompaktheit in Dualräumenger
dc.title.alternativeCharacterizations of weak compactness in dual spaceseng
dc.typeDissertation oder Habilitation [doctoralThesis]-
thesis.locationOsnabrück-
thesis.institutionUniversität-
thesis.typeDissertation [thesis.doctoral]-
thesis.date2003-08-13T12:00:00Z-
elib.elibid245-
elib.marc.edtfangmeier-
elib.dct.accessRightsa-
elib.dct.created2003-08-29T18:57:50Z-
elib.dct.modified2003-09-15T19:56:27Z-
dc.contributor.refereeProf.Dr. Egon Scheffold
dc.subject.msc46B40eng
dc.subject.msc46B42eng
dc.subject.msc46B50eng
dc.subject.msc28B05eng
dc.subject.msc47B65eng
dc.subject.dnb27 - Mathematikger
vCard.ORGFB6ger
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