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Lower and upper 2-estimates for order bounded sequences and Dunford-Pettis operators between certain classes of Banach lattices

Part of the Lecture Notes in Mathematics book series (LNM,volume 1470)

Abstract

We introduce the class of weak Schur spaces, i.e., Banach lattices in which relatively weakly compact sets and almost order bounded sets coincide. There follows a detailed study of Banach lattices in which every semi-normalized, order bounded, weakly null sequence contains a subsequence satisfying a lower, resp. an upper, 2-estimate. From the previous results we obtain conditions under which non-Dunford-Pettis operators between certain classes of Banach lattices fix a copy of ℓ2.

Keywords

  • Banach Lattice
  • Order Interval
  • Orlicz Function
  • Null Sequence
  • Unit Vector Basis

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Work on this paper was supported by Deutsche Forschungsgemeinschaft DFG.

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© 1991 Springer-Verlag

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Räbiger, F. (1991). Lower and upper 2-estimates for order bounded sequences and Dunford-Pettis operators between certain classes of Banach lattices. In: Odwell, E.E., Rosenthal, H.P. (eds) Functional Analysis. Lecture Notes in Mathematics, vol 1470. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090219

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  • DOI: https://doi.org/10.1007/BFb0090219

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54206-3

  • Online ISBN: 978-3-540-47493-7

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