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

 

Lower $ 2$-estimates for sequences in Banach lattices


Author: Frank Räbiger
Journal: Proc. Amer. Math. Soc. 111 (1991), 81-83
MSC: Primary 46B42; Secondary 46B15
MathSciNet review: 1023354
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Abstract: We characterize Banach lattices in which every bounded sequence contains a subsequence which either converges in norm or satisfies a lower $ 2$-estimate. As a consequence we obtain, for the class of all Banach lattices, a positive answer to a question of D.J. Aldous and D.H. Fremlin whether a Banach space of cotype 2 satisfies the above-mentioned property.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1023354-9
PII: S 0002-9939(1991)1023354-9
Keywords: Banach lattice, lower $ 2$-estimate, cotype 2
Article copyright: © Copyright 1991 American Mathematical Society