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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.


References [Enhancements On Off] (What's this?)

  • [1] D. J. Aldous and D. H. Fremlin, Colacunary sequences in 𝐿-spaces, Studia Math. 71 (1981/82), no. 3, 297–304. MR 667318
  • [2] Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. I, Springer-Verlag, Berlin-New York, 1977. Sequence spaces; Ergebnisse der Mathematik und ihrer Grenzgebiete, Vol. 92. MR 0500056
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  • [4] 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, 10.1007/BFb0090219

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1023354-9
Keywords: Banach lattice, lower $ 2$-estimate, cotype 2
Article copyright: © Copyright 1991 American Mathematical Society