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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
DOI: https://doi.org/10.1090/S0002-9939-1991-1023354-9
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 (1982), 297-304. MR 667318 (83j:46025)
  • [2] J. Lindenstrauss and L. Tzafriri, Classical Banach spaces I. Sequence spaces, Springer-Verlag, Berlin, Heidelberg, and New York, 1977. MR 0500056 (58:17766)
  • [3] -, Classical Banach Spaces II. Function spaces, Springer-Verlag, Berlin, Heidelberg, and New York, 1979. MR 540367 (81c:46001)
  • [4] F. Räbiger, Lower and upper $ 2$-estimates for order bounded sequences and Dunford-Pettis operators between certain classes of Banach lattices (Proc. Univ. of Texas at Austin 1987-1989), Lecture Notes in Math, Springer-Verlag (to appear). MR 1126744 (92j:47068)

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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

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