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Operator-valued measures and linear operators |
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| Authors: | Marian Nowak |
| Institution: | Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, ul. Szafrana 4A, 65-516 Zielona Góra, Poland |
| Abstract: | We study operator-valued measures  , where L(X,Y) 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. |
| Keywords: | Vector measures Operator-valued measures Mackey topologies Radon-Nikodym property Strong operator topology Weak operator topology Weak&lowast operator topology Linear operators |
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