Title:	Charakterisierungen schwacher Kompaktheit in Dualräumen
Other Titles:	Characterizations of weak compactness in dual spaces
Authors:	Möller, Christian
Thesis advisor:	Prof. Dr. Peter Meyer-Nieberg
Thesis referee:	Prof.Dr. Egon Scheffold
Abstract:	In 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.
URL:	https://osnadocs.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2003091515
Subject Keywords:	weak compactness; M-space with an order unit; dual space; Schur property; Rosenthal´s Lemma; (order-)weakly compact operator; Vitali-Hahn-Saks theorem
Issue Date:	15-Sep-2003
Submission date:	15-Sep-2003
Type of publication:	Dissertation oder Habilitation [doctoralThesis]
Appears in Collections:	FB06 - E-Dissertationen

Items in osnaDocs repository are protected by copyright, with all rights reserved, unless otherwise indicated. rightsstatements.org