Lower 2-estimates for sequences in Banach lattices

Räbiger, Frank

doi:10.1090/S0002-9939-1991-1023354-9

Lower $2$-estimates for sequences in Banach lattices
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Proc. Amer. Math. Soc. 111 (1991), 81-83 Request permission

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.

References

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Frank Räbiger, Lower and upper $2$-estimates for order bounded sequences and Dunford-Pettis operators between certain classes of Banach lattices, Functional analysis (Austin, TX, 1987/1989) Lecture Notes in Math., vol. 1470, Springer, Berlin, 1991, pp. 159–170. MR 1126744, DOI 10.1007/BFb0090219