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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Relatively uniform Banach lattices
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by Andrew Wirth PDF
Proc. Amer. Math. Soc. 52 (1975), 178-180 Request permission

Abstract:

Sequential relative uniform and norm convergence agree in a Banach lattice, if and only if it is equivalent to an $M$ space.
References
  • Garrett Birkhoff, Lattice theory, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1967. MR 0227053
  • K. Knopp, Theory and application of infinite series, 2nd English ed., Blackie, London, 1951.
  • Solomon Leader, Sequential convergence in lattice groups, Problems in analysis (Sympos. dedicated to Salomon Bochner, Princeton Univ., Princeton, N.J., 1969) Princeton Univ. Press, Princeton, N.J., 1970, pp. 273–290. MR 0344842
  • A. C. Zaanen, Stability of order convergence and regularity in Riesz spaces, Studia Math. 31 (1968), 159–172. MR 240597, DOI 10.4064/sm-31-2-159-172
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • 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