1984 | OriginalPaper | Buchkapitel
The Josefson-Nissenzweig Theorem
verfasst von : Joseph Diestel
Erschienen in: Sequences and Series in Banach Spaces
Verlag: Springer New York
Enthalten in: Professional Book Archive
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From Alaoglu’s theorem and the F. Riesz theorem, we can conclude that for infinite-dimensional Banach spaces X the weak* topology and the norm topology in X* differ. Can they have the same convergent sequences? The answer is a resounding “no!” and it is the object of the present discussion. More precisely we will prove the following theorem independently discovered by B. Josef son and A. Nissenzweig.