Operator-valued measures and linear operators

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• 作者：Marian Nowak
• 关键词：Vector measures ; Operator-valued measures ; Mackey topologies ; Radon&#x2013 ; Nikodym property ; Strong operator topology ; Weak operator topology ; Weak^* operator topology ; Linear operators
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2008
• 出版时间：1 January 2008
• 年：2008
• 卷：337
• 期：1
• 页码：695-701
• 全文大小：152 K

文摘

We study operator-valued measures , where stands for the space of all continuous linear operators between real Banach spaces X and Y and Σ is a σ-algebra of sets. We extend the Bartle–Dunford–Schwartz theorem and the Orlicz–Pettis theorem for vector measures to the case of operator-valued measures. We generalize the classical Vitali–Hahn–Saks theorem to sets of operator-valued measures which are compact in the strong operator topology.