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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Dunford-Pettis operators and weak Radon-Nikodým sets

Author: Lawrence H. Riddle
Journal: Proc. Amer. Math. Soc. 91 (1984), 254-256
MSC: Primary 46B22; Secondary 46G10
MathSciNet review: 740180
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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\,$measurable$ ,\,\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.

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PII: S 0002-9939(1984)0740180-2
Keywords: Dunford-Pettis operators, weak Radon-Nikodým sets, Pettis integral
Article copyright: © Copyright 1984 American Mathematical Society