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Proceedings of the American Mathematical Society

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Banach lattice structures on separable $ L\sb{p}$ spaces

Authors: E. Lacey and P. Wojtaszczyk
Journal: Proc. Amer. Math. Soc. 54 (1976), 83-89
MathSciNet review: 0390743
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Abstract: A complete characterization of those lattice structures on separable $ {L_p}$ spaces which are Banach lattice structures under the $ {L_p}$ norm is given.

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

  • [1] Ju. A. Abramovič and P. Wojtaszczyk, On the uniqueness of order in spaces $ {l_p}$ and $ {L_p}[0,1](1 \leqslant p \leqslant \infty )$ (Russian) (to appear).
  • [2] L. E. Dor and E. Odell, Monotone bases in $ {L_p}$ (to appear).
  • [3] H. Elton Lacey, The isometric theory of classical Banach spaces, Springer-Verlag, New York-Heidelberg, 1974. Die Grundlehren der mathematischen Wissenschaften, Band 208. MR 0493279
  • [4] E. Lacey and P. Wojtaszczyk, Non-atomic $ M$ spaces can have $ {l_1}$ as a dual space (to appear).
  • [5] John Lamperti, On the isometries of certain function-spaces, Pacific J. Math. 8 (1958), 459–466. MR 0105017
  • [6] J. Lindenstrauss and A. Pełczyński, Contributions to the theory of the classical Banach spaces, J. Functional Analysis 8 (1971), 225–249. MR 0291772
  • [7] Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces, Lecture Notes in Mathematics, Vol. 338, Springer-Verlag, Berlin-New York, 1973. MR 0415253
  • [8] Peter Meyer-Nieberg, Charakterisierung einiger topologischer und ordnungstheoretischer Eigenschaften von Banachverbänden mit Hilfe disjunkter Folgen, Arch. Math. (Basel) 24 (1973), 640–647 (German). MR 0341021,

Additional Information

Keywords: Banach lattice, $ {L_p}$ space
Article copyright: © Copyright 1976 American Mathematical Society

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