The sum of two Radon-Nikodým-sets need not be a Radon-Nikodým-set

Author:
Walter Schachermayer

Journal:
Proc. Amer. Math. Soc. **95** (1985), 51-57

MSC:
Primary 46B22; Secondary 28B05, 46G10

MathSciNet review:
796445

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Abstract: It was shown by C. Stegall that, if is a Radon-Nikodym-set and weakly compact, then is a Radon-Nikodym-set. We show that there are closed, bounded, convex Radon-Nikodym-sets and such that is closed but contains an isometric copy of the unit-ball of . In fact, we give two examples, one following the lines of one due to McCartney and O'Brian, the other due to Bourgain and Delbaen. We also give an easy example of a non-Radon-Nikodym-set such that, for every , there is a Radon-Nikodym-set such that is contained in the sum of and the ball of radius .

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DOI:
https://doi.org/10.1090/S0002-9939-1985-0796445-2

Article copyright:
© Copyright 1985
American Mathematical Society