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Banach lattices with the subsequence splitting property


Author: Lutz W. Weis
Journal: Proc. Amer. Math. Soc. 105 (1989), 87-96
MSC: Primary 46B30
DOI: https://doi.org/10.1090/S0002-9939-1989-0937853-X
MathSciNet review: 937853
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Abstract: A Banach lattice $ X$ has SSP if every bounded sequence in $ X$ has a subsequence that splits into a $ X$-equi-integrable sequence and a sequence with pairwise disjoint support. We characterize such lattices in terms of uniform order continuity conditions and ultrapowers. This implies that rearrangement invariant function spaces with the Fatou-property have SSP.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0937853-X
Keywords: Equi-integrable sets, ultrapowers, rearrangement invariant function spaces
Article copyright: © Copyright 1989 American Mathematical Society

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