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
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