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Proceedings of the American Mathematical Society

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Relatively uniform Banach lattices


Author: Andrew Wirth
Journal: Proc. Amer. Math. Soc. 52 (1975), 178-180
MSC: Primary 46A40
DOI: https://doi.org/10.1090/S0002-9939-1975-0374862-6
MathSciNet review: 0374862
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Abstract: Sequential relative uniform and norm convergence agree in a Banach lattice, if and only if it is equivalent to an $ M$ space.


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

  • [1] L. G. Birkhoff, Lattice theory, 3rd ed., Amer. Math. Soc. Colloq. Publ., Vol. 25, Amer. Math. Soc., Providence, R. I., 1967. MR 37 #2638. MR 0227053 (37:2638)
  • [2] K. Knopp, Theory and application of infinite series, 2nd English ed., Blackie, London, 1951.
  • [3] S. Leader, Sequential convergence in lattice groups, Problems in Analysis, (R. C. Gunning, editor), Princeton, 1970, pp. 273-290. MR 0344842 (49:9581)
  • [4] A. C. Zaanen, Stability of order convergence and regularity in Riesz spaces, Studia Math. 31 (1968), 159-172. MR 39 #1944. MR 0240597 (39:1944)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0374862-6
Keywords: Banach lattice, relative uniform convergence, order convergence, $ M$ space, $ {L^P}$ space
Article copyright: © Copyright 1975 American Mathematical Society

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