Vector measures and Mackey topologies

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• 作者：Marian Nowak ^{M.Nowak@wmie.uz.zgora.pl}
• 关键词：Bounded measurable functions ; ¦Ò-smooth operators ; Mackey topologies ; Strongly Mackey space ; Weakly compact operators ; Countably additive measures ; Strict Dunford&ndash ; Pettis property
• 刊名：Indagationes Mathematicae
• 出版年：2012
• 出版时间：March 2012
• 年：2012
• 卷：23
• 期：1-2
• 页码：113-122
• 全文大小：206 K

文摘

Let be a -algebra of subsets of a non-empty set . Let be the Banach lattice of all bounded -measurable real-valued functions defined on , equipped with the natural Mackey topology . We study -continuous linear operators from to a quasicomplete locally convex space . A generalized Nikodym convergence theorem and a Vitali-Hahn-Saks type theorem for operators on are obtained. It is shown that the space has the strict Dunford-Pettis property. Moreover, a Yosida-Hewitt type decomposition for weakly compact operators on is given.