Dunford-Pettis operators and weak Radon-Nikodým sets
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- by Lawrence H. Riddle PDF
- Proc. Amer. Math. Soc. 91 (1984), 254-256 Request permission
Abstract:
Let $K$ be a weak*-compact convex subset of a Banach space $X$. If every Dunford-Pettis operator from ${L_1}\left [ {0,1} \right ]$ into ${X^ * }$ that maps the set $\{ \chi E/\mu (E):E \text {measurable}, \mu (E) > 0\}$ into $K$ has a Pettis derivative, then $K$ is a weak Radon-Nikodým set. This positive answer to a question of M. Talagrand localizes a result of E. Saab.References
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Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 91 (1984), 254-256
- MSC: Primary 46B22; Secondary 46G10
- DOI: https://doi.org/10.1090/S0002-9939-1984-0740180-2
- MathSciNet review: 740180